Came back to review how to change limits of integration when doing U-substitution. This was a quick and simple way to get exactly the information I was looking for. Thanks.
@IntellectualPopulist I believe he divided the du by 3 and then just plugged the du into the equation, which somehow cancels out like dx does. If that made any sense at all . . . It's around the first minute of the video. You just have to pay close attention to what he's doing
I am just preparing for next term (which starts in a week). I was able to get an A in Calc 1 because of your videos. Figured I would start studying a little earlier because everyone is telling me that calc 2 is SO Much harder than calc 1.
your teaching is one of the clearest I've come across. Please become a math professor and teach at my university!!....we have some really shitty math profs where I am....
Ha, I actually spent a few minutes looking for this video! Seeing the giant white board (versus your smaller one or paper) threw me off, heh.
I'm incredibly grateful for all you do though. Math has always been a bit difficult for me, but everything you've done has made it so much easier...and pleasant! Thank you so much =)
@TheSrrobinson nevermind I see how this works out. I see how changing the bounds of integration with respect to "u" allows us to not need to plug in the original value for "u". Also, I see that if you keep the bounds the same then one would need to plug in the x^3 + 1 value replacing "u" to finish solving. Eureka!
I have a final in 7 hours and have been struggling to grasp this concept for the past two weeks. Thanks to your video I finally get it, thanks a bunch and keep the videos coming!
@patrickJMT don't you need to put u back in terms of x after you find the antiderivative? and then evaluate at the limits? like (9^3 + 1)^11 etc... yes? no? god im confused
@searching4somewhere i had the same question. If you do not change the bounds of integration then you would need to plug in x^3+1 for 'u'. However, since patrickJMT changed the bounds of integration with respect to 'u', we can simply plug in the new bounds for 'u'. Try doing it both ways, and you will get the same answer.
@TheSrrobinson Thanks for clearing that up, I was actually doing some problems today and kind of figured it out on my own. But im probably going to forget how it works anyway lol
You're amazing, your videos are the only ones I've found (after searching for a good amount of time) that have really connected the topics for me. Thank you =)
I did think that you had to include the Constant of Integration but I didn't think you had to since you had a definite answer? (Is that the right term or? Not sure =/ )
Since our answer is 186 there is no + C right? maybe?
By the way I'm only 14 so I was just wondering if what I did was right =)
You would if you weren't looking for area. Of it's a definite integral, you can leave your variables in "u" and plug in those bounds.
You CAN go back to x's by subbing in the x^3+1 for u, but you would have to change your bounds back to 1 and 2, so it's easier to leave it in u's for definite integrals and you get the same answer.
dude, god bless ya , you are the man , i love that you use short cuts and you make your videos as short and as informative as possible , i don't know but some teachers talk maths like it is symbols or something , they keep saying things like (if and only if , let R>>>C ) and such nonsense and i think it turns many people off from the beautiful world of math.
Your videos have been very helpful for my Calculus class. I have one question. Can you tell me why in the first example the limits of integration are 1 and 2 are no longer valid. Is it because its 1/3 du that is equal to x^2dx? Thanks!
I'm a 2nd year university student who was working on some first year math review. Thanks to your tutorial, I am now able to understand how to do u substitution with definite integrals ! :D
my ass is saved! Thank you so much as always, I can't believe the wealth of knowledge that you have on here...I wish I would have found out about your vids during calc 1....there are others, but the way you explain things is so comfortable and easy to listen to and understand. I bet you make a hell of a teacher!
Love your video, I like the HD ones more :) but everything great, even your voice is nice to listen to.. I got a calculus final tomorrow, and I feel a lot more comfortable after watching your videos.
@patrickJMT With definite integrals can you just plug the original value for U back in and then solve using the original limits without having to calculate the new values limits for the U integral?
@eoterm I've watched his vids before all of my calc tests and have made As on all of them so far lol. Pretty good considering i go to calc maybe once a week.
Patrick, thanks so much man, it's 3am here in AZ and I've been up all night studying for my calc 1 final. You've helped so much! hopefully i get above an 85 (which is what i need to sustain my A)!!
Haha I don't think too many people do know what 9^11 is off the top of their head. Daniel Tammet probably does though. If you don't know who he is search "The boy with the incredible brain" on youtube.
I was very sick and missed a good deal of time at school. An hour ago, I was in tears because none of my classmates take notes or care about calc, so I was in trouble. Thank-you so much! You really help out the people who try in class and want to work hard, and you help the people who need a different method of learning calculus than what their teachers may teach. God bless you!
i think criticism is humbling. unfortunately, there is never anything to complain about with these videos. but this time, i have noticed something. i prefer paper to white board. lol. there, i said it. i found something i actually would change. besides that, its perfect. keep it up! for my education's sake.
yea...i was gonna ask you sometime where you get all of your paper from...because you go through so much just making these vids, lol.
I too prefer the paper or the tiny white board that you use, instead of this bigger white board....it just makes it seem like you are a tutor that's helping me 1 on 1, instead of the teacher showing the whole class.
Apart from that, there's nothing else to complain about; your videos are always very helpful
You are the man! I am wondering why the limits of integration 1 to 2 are no longer valid when using u's in this problem? Is this always the case or just in this example?
brother note that limit of integration are changed in all definit integal substitution while it remain same in the indefinit integral subsitution method
so once you change your limits with respect to 'u' you can just plug those limits in for 'u'? i might be wrong but i remember being taught that you can keep the same limits and then just plug the original equation that contained x in it for u, and then evaluate your anti-derivative at your original limits... does that work too?
Fantastic explanation of u-substitution for definite integrals. Thanks so much for taking the time to post something like this on YouTube to help us all. Your explanation was clear and easy to follow, and the added complexity of the 1/3 term really helped clarify how useful u-substitution can be even when the derivative of the u term doesn't appear exactly in the formula.
Thankyou VERY much for your help. Your explanations were very clear and have solved alot of my integration problems! It feels like a door to the harder questions has been opened up!
Im not as worried for tomorrows exam anymore =D Whooo!
the 1/3 comes because We're no longer defining this function in terms of "x" but in terms of a different variable "u". However, in order for the two expressions to remain equal, we need to alter some of the integral's expressions, otherwise our substitution is quite pointless.
the 1/3 just comes because he distributed it out of the expression as what was formerly x2 dx, then became 1/3 du.
since he had a x^2 and a dx in da original equation. he minipulated du=3x^2.dx using algebra so he got 1/3du=x^2.dx. he just divided both sides by 3. so he gt x^2.dx on the r.h.s. he just replaced the x^2.dx by 1/3du in the original equation. does that make sense??? lol
man both sides are divided by 3. and then when integrating he factored it out, because it is a constant. man look what he did in blue to know what happed to x^2, it is replaced by du.
thanks alot for the video, but it could be done without having to look for a new limits. its even more complicated trying to look for a new limits. thnx:)
well, eventually, when one starts doing multiple substitutions or multiple integrals, it is easier to find new limits as you go, so one needs to see it in order to do those problems!!
What's the difference in calculating the new limits before as opposed to just putting the old limits back in later. So after intergrating .. your equation would be:
1/3 * (x^3 + 1)^11 / 11 .... if you plug in 2 and 1 as x now ... you'll get 9 and 2 ... that's the exact same thing. I don't get the need for finding new limits ahead of time.
You're absolutely right. You can do one or the other, like a previous comment says. Changing the limits of integration just makes it so you don't have to change u back to what it was before. But if you change u back, you can leave the limits of integration alone. Do one or the other, whichever you prefer.
OK, still my question is Where did the 3x^2 come from???? Why did he choose 3??? Will always choose 3?? Or can a just pull a number out of the clear blue yonder??? I see everything else in the problem except where on earth the 3 comes from????
when you let "u"= "something", that "something" has to be pluged in to u
after when you take the integral.if you don't, you are just taking the integral of u, not the integral of that funtion. So, the function has to be pluged in to U.
u no how first his got like 1-2 for the x, then he changed it to 2-9....its because he already put in that equation for the new numbers, so thats y he didnt plug in the equation in the end. You can do one or the other!
one question... after you integrate and get u^11/33, why don't you plug in x^3+1 for u. I'm wondering, is it because the derivative is with respect to du, not dx?
I started studying for my calculus 1 exam on 1/1/2009 just by watching all your videos about integration and series without having any classes at all! Yesterday i did the exam... guess what? I think it went really well!! I recommend your channel to all my friends who are having difficulties with calculus ;)
quick question, once you have your U after taking the anti-derivative, couldnt you just plug back in what U was in terms of X and then evaluate it at the old lower and upper limits of integration rather than finding new ones as that is what I'm taught to do
PURE OWNAGE, what I needed, the dang change in limits after a u substitution, one problem... is there an example with changing to trigo? the limits will have to change to angles... which may pose difficulties for certain questions...
I'm a math prof and I appreciate the care with which you explain the process. I even gave a link for this to my class of biology majors for a well-worked out example with good tips too.
I took this stuff about a month ago and your explanation is so easy and helpul. All the instructors I get love to RUSH and make it so hard when its not. So basically what I'm saying is, I wish my instructors taught like you. Maybe you should give them a lesson.
Came back to review how to change limits of integration when doing U-substitution. This was a quick and simple way to get exactly the information I was looking for. Thanks.
v33nx0r 1 week ago
@v33nx0r perfect :) i actually now have a video about ' u - substitution , when do i change the limits of integration ' cause so many people aked
patrickJMT 1 week ago
this was sooooooo helpful! omg thank you:)
bitch17376 1 week ago
this video is the oldest out of the ones i watched
DragonRider520 3 weeks ago
How did he account for that first x^2 outside the quantity? From what I understand he only substituted the inside? Somebody must know.
IntellectualPopulist 1 month ago
@IntellectualPopulist I believe he divided the du by 3 and then just plugged the du into the equation, which somehow cancels out like dx does. If that made any sense at all . . . It's around the first minute of the video. You just have to pay close attention to what he's doing
Lumophage 1 week ago
That was nice!
I am just preparing for next term (which starts in a week). I was able to get an A in Calc 1 because of your videos. Figured I would start studying a little earlier because everyone is telling me that calc 2 is SO Much harder than calc 1.
Do you feel this is true?
Thanks,
From Oregon
wperlich 2 months ago in playlist Calculus / Second Semester - Integration
@wperlich integration is typically harder than differentiation, so yes, i think calc 2 is probably a bit more challenging
patrickJMT 2 months ago
your teaching is one of the clearest I've come across. Please become a math professor and teach at my university!!....we have some really shitty math profs where I am....
pcd6music 2 months ago
Ha, I actually spent a few minutes looking for this video! Seeing the giant white board (versus your smaller one or paper) threw me off, heh.
I'm incredibly grateful for all you do though. Math has always been a bit difficult for me, but everything you've done has made it so much easier...and pleasant! Thank you so much =)
keetner 2 months ago
@patrickJMT Don't we need to plug x^3+1 back in for "u" to finish out the problem?
TheSrrobinson 2 months ago
@TheSrrobinson nevermind I see how this works out. I see how changing the bounds of integration with respect to "u" allows us to not need to plug in the original value for "u". Also, I see that if you keep the bounds the same then one would need to plug in the x^3 + 1 value replacing "u" to finish solving. Eureka!
TheSrrobinson 2 months ago
I have a final in 7 hours and have been struggling to grasp this concept for the past two weeks. Thanks to your video I finally get it, thanks a bunch and keep the videos coming!
cjsoccer09 2 months ago
@patrickJMT don't you need to put u back in terms of x after you find the antiderivative? and then evaluate at the limits? like (9^3 + 1)^11 etc... yes? no? god im confused
searching4somewhere 2 months ago
@searching4somewhere i had the same question. If you do not change the bounds of integration then you would need to plug in x^3+1 for 'u'. However, since patrickJMT changed the bounds of integration with respect to 'u', we can simply plug in the new bounds for 'u'. Try doing it both ways, and you will get the same answer.
TheSrrobinson 2 months ago
@TheSrrobinson Thanks for clearing that up, I was actually doing some problems today and kind of figured it out on my own. But im probably going to forget how it works anyway lol
searching4somewhere 2 months ago
what happened to "+ C"
eyeheartthekillers 2 months ago
@eyeheartthekillers you do not need it for definite integrals. i just cancels out when we subtract so people do not bother including it
patrickJMT 2 months ago 13
@eyeheartthekillers
It's a definite Integral, which is an exact value, so no +c is necessary.
DaveBandfanMatthews 1 month ago
U=awesome(x)
dU=totallyawesome(dx)
AnthonyPickett 2 months ago
You are a lifesaver!! Thank you so much for taking the time to share your knowledge, for free! :)
melkoch01 2 months ago
Thank you so much!
CSCCoder 3 months ago
you saved my ass so many times
TehRice 3 months ago
thank you so so so so so so much! i learned more in an hour watching your videos than a whole month in my calc teacher's lectures...
and i think you're much better than khan academy :)
jmwChan 3 months ago
You're amazing, your videos are the only ones I've found (after searching for a good amount of time) that have really connected the topics for me. Thank you =)
Sharylyn13 3 months ago
@Sharylyn13 come back and watch any time ; )
patrickJMT 3 months ago
@patrickJMT wat a playa lol
frojabotta 3 months ago
I did think that you had to include the Constant of Integration but I didn't think you had to since you had a definite answer? (Is that the right term or? Not sure =/ )
Since our answer is 186 there is no + C right? maybe?
By the way I'm only 14 so I was just wondering if what I did was right =)
Please reply if you can? =)
Thanks =)
joshua99999999 5 months ago
Hey PatricJMT - I have a question that would be nice if you could answer:
When you write out the equation with integration and expansion, How do you continue to break the equation down? - For example
[Int - 0 -> 3] 2x (x^3 + 4) dx
I understand that with 'U' substitution you replace (x^3 + 4) with U right - but do you just cancel out the equation and do this? :
2x^4 + 8x du ?
and then
186 - 0 ?
with the resulting answer being 186? - And you don't take away anything as 2x0^4 + 8x0 = 0?
joshua99999999 5 months ago
You're a great teacher. :)) Thanks!
lendylovescandy 6 months ago
thanks
na9oooooooor 7 months ago
you just got another subscriber, thanks much!
popbottlerockets 7 months ago in playlist Calc II Final
I want to sex your face right now....this video just saved my grade on my quiz
loquaciousman 7 months ago
boo mormon commercials
neilcwright 8 months ago
u r my hero
Gazzawey 9 months ago
@KoreaXFan
You would if you weren't looking for area. Of it's a definite integral, you can leave your variables in "u" and plug in those bounds.
You CAN go back to x's by subbing in the x^3+1 for u, but you would have to change your bounds back to 1 and 2, so it's easier to leave it in u's for definite integrals and you get the same answer.
Chiborino 9 months ago
oh man i wish i had discovered these videos earlier in the school year.... they would have saved me a LOT of stress
nataliegiraffe 10 months ago
Calculus is fun
ONLY if u know wut the hell to do
themanso08 10 months ago
good vid but i reckon you should teach the derivative outside theorum! e.g. the 1/(n+1)f(x)^(n+1)
fionaNESS 10 months ago
At the end of the video don't you first place back in the u = x^3 + 1, then you add in the 9 and 2?
KoreaXFan 10 months ago
This was EXTREMELY helpful, Thank you so so so much
Ladyphia7 10 months ago
You're the Jesus of Calculus
Hockeyrocks229 11 months ago 2
dude, god bless ya , you are the man , i love that you use short cuts and you make your videos as short and as informative as possible , i don't know but some teachers talk maths like it is symbols or something , they keep saying things like (if and only if , let R>>>C ) and such nonsense and i think it turns many people off from the beautiful world of math.
zidan40o0 11 months ago
Seriously man, I love you. Straightforward, easy to follow, and I don't fall asleep, which is way more than I can say about my calculus class.
righthandmafioso 1 year ago
can i ask why do we need a new limit when we integrated it and the limit 1 to 2 is no longer valid? thank you so much
orangejuicerox 1 year ago
Comment removed
DJCrabCake 1 year ago
you make my calculus professor look like a genetically mutated Neanderthal
TheJoshlav 1 year ago
would the answer to the u-substituted part of the integration be multiplied by the integration of the x^2,x,1,2?
spnsdr 1 year ago
is it okay if i say that they way you teach is oh so magical? omg xD
d3mur3 1 year ago
omg sooo helpful
da1ndonlylinda 1 year ago
Dude his arms are so veiny and kind of muscular *giggles*
bvlgary09 1 year ago
I LOVE YOU.
radgirl21 1 year ago
has anyone ever seen his face?
MrMig3 1 year ago
@MrMig3 I think the background of his Channel has a picture of him. Lol, you can see his face there?
nutella871 1 year ago
Your videos have been very helpful for my Calculus class. I have one question. Can you tell me why in the first example the limits of integration are 1 and 2 are no longer valid. Is it because its 1/3 du that is equal to x^2dx? Thanks!
harriscrl3 1 year ago
this is great!!!!! XD thank u!!
erikationofkita 1 year ago
Thumbs up
anibaze 1 year ago
You just made my life so much easier XD
michicacue 1 year ago
Comment removed
ahladdin2403 1 year ago
I'm a 2nd year university student who was working on some first year math review. Thanks to your tutorial, I am now able to understand how to do u substitution with definite integrals ! :D
azntranc3951 1 year ago
I don't know what 9^11 is, maybe you do... love the subtle humor
resevil787 1 year ago
my ass is saved! Thank you so much as always, I can't believe the wealth of knowledge that you have on here...I wish I would have found out about your vids during calc 1....there are others, but the way you explain things is so comfortable and easy to listen to and understand. I bet you make a hell of a teacher!
mpatt79 1 year ago
You saved my ass in calc I, thank u very much
socialdice13 1 year ago
3hours of trying to figure this out just figure it out in 4:47 because of you..thank you
btfrempo 1 year ago
u r gr8 !!!! thnx ..
Danasqu 1 year ago
Love your video, I like the HD ones more :) but everything great, even your voice is nice to listen to.. I got a calculus final tomorrow, and I feel a lot more comfortable after watching your videos.
Thank you so much
eoterm 1 year ago 20
@eoterm yes, this was one of the very first videos i made - no HD camera at that time : )
patrickJMT 1 year ago
@patrickJMT With definite integrals can you just plug the original value for U back in and then solve using the original limits without having to calculate the new values limits for the U integral?
IGNsucks 1 year ago
@IGNsucks yep!
patrickJMT 1 year ago 3
@eoterm I've watched his vids before all of my calc tests and have made As on all of them so far lol. Pretty good considering i go to calc maybe once a week.
aakashisme 1 year ago
@eoterm can someone please tell me why it is so useful learn calculus fro real life apllications
when will it come in handy?
TheCasao86 9 months ago
i was wondering in what age does integration being teach to students in US?
in my country it was 17 . some one answering?
TheBlueEmperor 1 year ago
This series on integration filled in all the pieces that I didn't get in lectures. Thank you for your time preparing these.
19bluejay67 1 year ago
Patrick, thanks so much man, it's 3am here in AZ and I've been up all night studying for my calc 1 final. You've helped so much! hopefully i get above an 85 (which is what i need to sustain my A)!!
resevil787 1 year ago 2
@resevil787 i assume the final was today... i hope it went well!
patrickJMT 1 year ago
@patrickJMT yessir, got an 86, which kept me at a 90 for the semester. Thanks again man!
resevil787 1 year ago
You just saved me! (As always!) :) Thanks a million
valsera246 1 year ago 2
Haha I don't think too many people do know what 9^11 is off the top of their head. Daniel Tammet probably does though. If you don't know who he is search "The boy with the incredible brain" on youtube.
BogMonkey53 1 year ago
thanks for the video. you make it seem so easy
TheSlayer42088 1 year ago
I was very sick and missed a good deal of time at school. An hour ago, I was in tears because none of my classmates take notes or care about calc, so I was in trouble. Thank-you so much! You really help out the people who try in class and want to work hard, and you help the people who need a different method of learning calculus than what their teachers may teach. God bless you!
8WingedAngel 1 year ago 14
@8WingedAngel khanacademy is another good online teacher.
BogMonkey53 1 year ago
you saved ass for my test tomorrow, thanks buddy!
Brew805 1 year ago 2
Again, you have shed light on a concept that seemed complicated. However, with you my friend, nothing is complicated. Thank you.
flaco954 1 year ago
Thumbs up! Thank you for taking the time to explain this so clearly.
Mike01010011 1 year ago
You are an awesome person. I like your videos.
Atomsk24 2 years ago
sry but if u is x^3 then u´ is 3x^2.
so you have to multiple the integral with 3 not with 1/3 or not???
MrFloydCouncil 2 years ago
do you always change the limits everytime you use u-sub?
mnava19 2 years ago
you are so cute patrick
sullivanseven 2 years ago
1:26
I like your spin technique it somehow helped
janitarjanitar 2 years ago
@janitarjanitar lol
sotoj159 2 years ago
Comment removed
janitarjanitar 2 years ago
This is way better than reading explanations from a book
kayloo4242 2 years ago
thanks sir these are very helpful for us. i am learning calculus from ur videos
arshadkhanize 2 years ago
Ehm how do you do (9)^11 without a calculator lolz
Aaroenz0r 2 years ago
@Aaroenz0r 9*9*9*9*9*9*9*9*9*9*9... Just do long multiplication. Old school elementary style. =P
wisigothx 2 years ago
why didn't I find this channel 2 years ago? my math problems would have disappeared by now.
Great videos; you do it better than all of my teachers. I have some grade raising to do!
Neverdii 2 years ago
i think criticism is humbling. unfortunately, there is never anything to complain about with these videos. but this time, i have noticed something. i prefer paper to white board. lol. there, i said it. i found something i actually would change. besides that, its perfect. keep it up! for my education's sake.
jayr64 2 years ago 6
well, i prefer paper actually too, but it seems so wasteful
patrickJMT 2 years ago
Just recycle, and your videos are gold! =]
gdistheshiz 2 years ago
@patrickJMT
yea...i was gonna ask you sometime where you get all of your paper from...because you go through so much just making these vids, lol.
I too prefer the paper or the tiny white board that you use, instead of this bigger white board....it just makes it seem like you are a tutor that's helping me 1 on 1, instead of the teacher showing the whole class.
Apart from that, there's nothing else to complain about; your videos are always very helpful
sotoj159 2 years ago
thank you very very much...
peterpatalano 2 years ago
ur smart
babygurl25392 2 years ago
You are the man! I am wondering why the limits of integration 1 to 2 are no longer valid when using u's in this problem? Is this always the case or just in this example?
Thanks for your help.. Your videos rock!
bkpoulsen 2 years ago
brother note that limit of integration are changed in all definit integal substitution while it remain same in the indefinit integral subsitution method
arshadkhanize 2 years ago
i would like to see [integral sign pie =b 0=a (sin(x)+cos(2x))dx] im stuck on that problem
or is there a video that already addresses that?
Brain704 2 years ago
I think you're antiderivative is -cosx + (sin 2x)/2
jonathan13piano 2 years ago
your better than my calculus teacher
luisr12491 2 years ago 44
amen
Shadowreaper5 2 years ago 2
his better then all our calculus teacher lol i don't eeven know wat topic were doing in our class
lena11sandy 2 years ago
@luisr12491 yeah i would agree
rachetclank94 1 year ago
Thanks for the video. It helped me on my homework.
luisr12491 2 years ago 2
so once you change your limits with respect to 'u' you can just plug those limits in for 'u'? i might be wrong but i remember being taught that you can keep the same limits and then just plug the original equation that contained x in it for u, and then evaluate your anti-derivative at your original limits... does that work too?
yumyum210 2 years ago
Fantastic explanation of u-substitution for definite integrals. Thanks so much for taking the time to post something like this on YouTube to help us all. Your explanation was clear and easy to follow, and the added complexity of the 1/3 term really helped clarify how useful u-substitution can be even when the derivative of the u term doesn't appear exactly in the formula.
Ilsem 2 years ago 2
great* even
alchemitch 2 years ago
your a lefty too :P grat vid btw. covers u subbing well
alchemitch 2 years ago 3
THANK YOU for your videos!!!!!!!!!
p3destrian 2 years ago 2
I LOVE YOU.
xB1ATCH 2 years ago 3
Thankyou VERY much for your help. Your explanations were very clear and have solved alot of my integration problems! It feels like a door to the harder questions has been opened up!
Im not as worried for tomorrows exam anymore =D Whooo!
squishinicci 2 years ago
I like that you included the new limits-that mistake cost me 2 points on a midterm.
Boomr616 2 years ago
Well explained. Thanks!
ednodes 2 years ago
im really confused as to where the 1/3 came from and where the x^2 went ?
notchloe 2 years ago
the 1/3 comes because We're no longer defining this function in terms of "x" but in terms of a different variable "u". However, in order for the two expressions to remain equal, we need to alter some of the integral's expressions, otherwise our substitution is quite pointless.
the 1/3 just comes because he distributed it out of the expression as what was formerly x2 dx, then became 1/3 du.
iridethewave 2 years ago
since he had a x^2 and a dx in da original equation. he minipulated du=3x^2.dx using algebra so he got 1/3du=x^2.dx. he just divided both sides by 3. so he gt x^2.dx on the r.h.s. he just replaced the x^2.dx by 1/3du in the original equation. does that make sense??? lol
asianpride3 2 years ago
man both sides are divided by 3. and then when integrating he factored it out, because it is a constant. man look what he did in blue to know what happed to x^2, it is replaced by du.
HeresSeem 2 years ago
thanks alot for the video, but it could be done without having to look for a new limits. its even more complicated trying to look for a new limits. thnx:)
abusisunju 2 years ago
well, eventually, when one starts doing multiple substitutions or multiple integrals, it is easier to find new limits as you go, so one needs to see it in order to do those problems!!
patrickJMT 2 years ago
This took my teacher a week to explain. I just got it in a few minutes...THANK YOU!!!
hugs4harry 2 years ago 2
thanks so much. my math teacher is horrible at explaining things in understandable terms and you're so good at it. Thanks for the help!
snowystarshine 2 years ago 2
What's the difference in calculating the new limits before as opposed to just putting the old limits back in later. So after intergrating .. your equation would be:
1/3 * (x^3 + 1)^11 / 11 .... if you plug in 2 and 1 as x now ... you'll get 9 and 2 ... that's the exact same thing. I don't get the need for finding new limits ahead of time.
StreekDime 2 years ago
You're absolutely right. You can do one or the other, like a previous comment says. Changing the limits of integration just makes it so you don't have to change u back to what it was before. But if you change u back, you can leave the limits of integration alone. Do one or the other, whichever you prefer.
KibaWolfe 2 years ago
OK, still my question is Where did the 3x^2 come from???? Why did he choose 3??? Will always choose 3?? Or can a just pull a number out of the clear blue yonder??? I see everything else in the problem except where on earth the 3 comes from????
BellaDaizy 2 years ago
3x^2 is the derivative of ( x^3 + 1) .....bring down the power infront of x and then subtract 1 from the top...... hope your familiar with it
irfaanfaki 2 years ago
3x^(2) came from the derivative from the x^(3)+1 term, which is = u.
BButterz88 2 years ago
3x^2 is du
u is x^3+1 so du/dx is the derivative of that,
manipulating that gives du=3x^2 dx
he just moved the dx to the other side
hplovepho 2 years ago
3x^2 is the derivative of u=x^3
potts0518 2 years ago
3x^2 is the derivative of (x^3 + 1).
mikeknowsbest 2 years ago
OMG!! Thank you Thank you Thank you Thank you Thank you Thank you Thank you!!!!! This is great. The best on youtube by far.
shallwedance88h 2 years ago 4
thank you VERY much.. you are a life saver.. i really appreciate your videos.. thanks again
sudaniq 2 years ago
Mr Patrick is know his stufffffff.
manzoor1 3 years ago
yeah, can someone please explain to me why you don't plug in ( x^3 + 1) back into the fxn?
btw, you're awesome! this is the first day i watched ur vids, and i get everything =]
ive watched like 3 so far
Jae132 3 years ago
when you let "u"= "something", that "something" has to be pluged in to u
after when you take the integral.if you don't, you are just taking the integral of u, not the integral of that funtion. So, the function has to be pluged in to U.
manzoor1 3 years ago
but he changed the x from 1-2 to 2-9.
hbquanie 2 years ago
u no how first his got like 1-2 for the x, then he changed it to 2-9....its because he already put in that equation for the new numbers, so thats y he didnt plug in the equation in the end. You can do one or the other!
hbquanie 2 years ago
oooh cool =]
Jae132 2 years ago
do you have a video regarding def. integrals using Wallis' formula?
x0pauh 3 years ago
i actually understand it better! but i still feel stupid in class yay...
no but really this helps a lot thank you
itzxclusive 3 years ago
This is amazing!! Your videos are soo hepful!! thank you sooooo much!!! Youtube isn't just full of random stupidity now.
wildwords7 3 years ago 14
one question... after you integrate and get u^11/33, why don't you plug in x^3+1 for u. I'm wondering, is it because the derivative is with respect to du, not dx?
tennisdrummerboy 3 years ago 2
nice muscles in the end lol
ubernoobert 3 years ago
lol, was i flexing? : ) i am soooooo jacked
patrickJMT 3 years ago
With an internet teacher like you who needs to go to classes?? 5*
dassseee 3 years ago 3
glad you like them and... go to class!! : )
patrickJMT 3 years ago
I started studying for my calculus 1 exam on 1/1/2009 just by watching all your videos about integration and series without having any classes at all! Yesterday i did the exam... guess what? I think it went really well!! I recommend your channel to all my friends who are having difficulties with calculus ;)
Thanks for everything!
dassseee 3 years ago
Great!
fauszayas1 3 years ago
lets give patrick the props he deserves - rate his vids!
cruthybabie 3 years ago
thanks
ericfeinberg28 3 years ago
quick question, once you have your U after taking the anti-derivative, couldnt you just plug back in what U was in terms of X and then evaluate it at the old lower and upper limits of integration rather than finding new ones as that is what I'm taught to do
SHAMIRMCLEISH 3 years ago
yes, absolutely you can do that!!
patrickJMT 3 years ago
coo sweet vid
SHAMIRMCLEISH 3 years ago
i was gona ask the same question.. but you already asked and he answered already! great video
itzonlydrea 3 years ago
Nevermind, same thing, just throw the whole thing together, NICE ONE, YOU'VE SAVED ME!!
toasterder 3 years ago
PURE OWNAGE, what I needed, the dang change in limits after a u substitution, one problem... is there an example with changing to trigo? the limits will have to change to angles... which may pose difficulties for certain questions...
toasterder 3 years ago
Great stuff, thanks
depiazbt 3 years ago
wow nice and clear explanation, thanks!
Salahuddin1 3 years ago
I'm a math prof and I appreciate the care with which you explain the process. I even gave a link for this to my class of biology majors for a well-worked out example with good tips too.
heropass 3 years ago
thanks for the kind words! i always appreciate hearing from a fellow teacher.
patrickJMT 3 years ago
: ) i am glad that my explanations help! i try to keep things as simple as possible!
patrickJMT 3 years ago
I took this stuff about a month ago and your explanation is so easy and helpul. All the instructors I get love to RUSH and make it so hard when its not. So basically what I'm saying is, I wish my instructors taught like you. Maybe you should give them a lesson.
platinumgv 3 years ago 2
Thank you
Scott25126 3 years ago
Thank you so much your video is so helpful
2erict 3 years ago