Improper Integral - More Complicated Example

[NickyNeu]

Couldn't you just use the tabular method for the IBP?

[buckeye2991]

Pat you cocky arrogant bastard! You act like you know everything and you're always writing in sharpie! Thanks for the help though!

[patrickJMT]

@buckeye2991 i just want you nice folks to be able to clearly see what i am writing :)

[AlanAbundis]

Patrick, when you make the indetermination (infinity*zero), shouldnt you write:( t)/(1/e^5t)? So that you get (infinity)/(1/zero)=(infinity)­/(infinity)

[mangomann786]

are you a school teacher by profession? 

[patrickJMT]

@mangomann786 nope, although i have taught a good bit in my life

[deeex4]

wait...so then, which one is your answer? 0 or 1/25?

[Eaturveggies21]

What book are you using for these examples because I notice some are in my "Calculus Early Transcendentals: James Stewart Volume 1" book.

[crazyhasek3921]

@patrickJMT if you are ever in New Jersey, I will take you on a free tour of our oil refineries/landfills and teach you how to party/rage. I am not serious.

[TeeEye84Plus]

You are very clear! I thoroughly understand every step and this is my first time seeing this stuff.

[Akwaterski]

PatrickJMT is a god among men. I understand everything you say the FIRST time through. If you ever are in Alaska, I will take you on a free tour/adventure, and teach you how to waterski. I'm dead serious.

[JoanieAtwater]

Patrick is my hero...

One thing to notice is that there's a pattern for these x^n*e^(-Ax) integrals.

all you need if you see this on a test is this: n! / A^(n+1)

Soooo in his example n=1 (the "s" raised to the first power) and A=5 (ignore the negative) plugging in his values: 1! / 5^(1+1) or 1/25

if this problem were: s^3*e^(-6s) then it's as easy as 3! / 6^(3+1) or 1/216

[danielvutran]

@JoanieAtwater Holy shit! LOL. Thanks a lot! This helped big time! ^.^

[gunmetalspecter]

Hey patrick, just wanted to say thank you for all your videos. I took precalc and calculus over the summer sessions at my colllege during the span of about 10 weeks. Without some of your videos I don't think I would be in calc II now. And to top it off I'm still being helped along the way with videos like this.

[PmQable1]

thanks patrick, you are a huge inspiration to me. i am currently in 9th grade geometry, but i understand all this stuff. you helped me so much with the stuff i didnt get straight out of my old calculus textbook. once again, thanks a lot.

[patrickJMT]

@PmQable1 absolutely my pleasure ; )

[Kratos0909]

This man deserves the Nobel peace prize..

[missgina916]

I understand..don't worry, there's no hard feelings. You just can't trust people nowadays. On a more serious note, I do want to say that you have an amazing gift in the way that you present the material in your tutorials. I've been watching your videos for a couple of months now, and I find myself teaching in a manner very similar to yours (I'm a tutor in the math lab on my college campus). I've improved not only as a student, but as a tutor as well, many thanks to you! You are much appreciated!

[missgina916]

Patrick, "Will You Marry Me?"

[patrickJMT]

@missgina916 probably not

[djbluelive]

Weird. You have some of the same mannerisms as my teacher... I wonder :) lol

[adobojo]

You wouldn't happen to be using the calculus textbook by James Stewart, would you? Just wondering. =)

[halflife1994]

dv must be "e^-5s ds" =)

[rawad2020]

man is there a chance to pass calculus II when I didnt study Calculus I >.>

[TheKingstoncowboy]

This is literally a question from my homework...lol...thanks dude.

[lncg10]

im so gonna send you a check when i get a professional job. Im pretty sure I've learned a lot more than what i've learned all semester from my professor.

[WrathofTim]

thank you for getting me through engineering

[integraleric]

I'll be sure to check out your channel. thanks.

[lobsidedballs]

It's Da Math Masta!



[Desimunda92]

Man, you're a math genius. I watched these improper integral videos and I got a 32/32 on my quiz a few days ago. Thank you so much dude!!!

[oOIDKOo]

Thanks so much for your videos they help out a lot! :D

I hate these ads..

[7thbrah]

LOL This is hilarious. The example you did is from MY TEXTBOOK. Section 6.6 Improper Integrals number 15. Nice. hahahah i cracked up. Red textbook with an integral on the front.

[wellitstrue102]

@7thbrah :O @patrickJMT you should definitely have done more from that book

[azimready]

Two calc teachers dont like their students getting A's on all their tests :P

[SAIL4323]

Why do use the letter s instead of x for the variable?

[flyordie2]

@SAIL4323 The various variable (or letter, such as x or s) can be used interchangeably. It does not matter which letter is used.

[bmdoubleuu]

how come we dont use the graph of e^-x when finding the limit of e^-5t?

[patrickJMT]

@Digidices well, i do try. i get tons of comments and messages though so i can not respond to all of them!

[alozonmo]

2 people are in arts and crafts (humanities)

[patrickJMT]

@alozonmo yes, cause things like history and art are just silly and worthless, right? whatever makes you feel good about yourself

[sarakitdotcom]

Thank you for your help, great explanation and step by step work!

[jayspenh]

thanks so much now i get it!

[jw111892]

why am i paying 28k tuition...

[patrickJMT]

@jw111892 price of education: going up. quality of education: going down (i'd wager). what a wonderful world: you get a larger debt with less skills to pay it off.

[honeypot11]

HAHA this was the exact problem that i got stuck on in the textbook before i went to look up your videos =D

awesome online tutor indeed C:

[patrickJMT]

@honeypot11 magical!

[rteyber]

you and you alone are getting me through integral calculus... Keep up the great vids!

[patrickJMT]

@rteyber i will try!

[gjohn1992]

forgot ds for the dv step. should be [e^(-5s)]ds

[XxardientexX]

it was so great!!! thanks!!! I understood all!!!

[shapeurmind]

L'Hopital!!! I guessed XD

[MissMarissaaaa]

Wow, how perfect...I was doing this exact same problem and didn't even think about L'Hospitals. Thanks!

[adamn3ve]

hi, i was wondering what a harmonic integral is?

and what do they mean when they ask you what value, say 'p', is when a harmonic integral 'I', is convergent?

would you use the same method as ur using for this improper integral?

[patrickJMT]

@oOKrazyKOo yes, these problems can have lots of different things going on, so i thought it best to do one

[lilmizzheather91]

I've quit going to class. Still getting an A. I should be paying you tuition.

[patrickJMT]

@lilmizzheather91 i accept checks and cash.

[tuto09]

@patrickJMT Hey pat why didn't you use tabular integration to solve the integral of s*e^-5x. Isn't easier then doing a tedious integration by parts?

[Genocide1812]

It's gotten to the point where I just go to class to learn the name of the subject and be confused, then youtube it and look for your name. Your 9 minute youtube videos are replacing - and effectively - 50 minute classes.

[patrickJMT]

@Genocide1812 try watching a video on the topic before you go to class; i think you will find you get much more out of the lecture.

[Genocide1812]

@patrickJMT Good idea

[TheFreshestDJ]

@Genocide1812 My thoughts exactly. My prof should just turn this youtube video on and leave, instead of attempting to teach.

[patrickJMT]

@TheFreshestDJ patrickjmt ftw

[varung92]

You are a lifesaver!!! Thanks a ton!!

[shoesies05]

great video... i would have gone right to the inf * 0 =0 forgeting about lhopitals rule.

[patrickJMT]

@jwmcmac or is it HER?

[FargandSirHomerlots]

THIS WAS SOOO MUCH HELP thank you. lol i havent really officially taken calc yet and this was really helpful for my summer assignment

[like9orphanz]

My goal is to buy you a beer one day.... one day......

[asaadalsabbagh]

thanks dude i really appreciate your work man

[patrickJMT]

@asaadalsabbagh happy to help

[abdullah57habib]

How come we don't write the +C when we conclude that the area is 1/25. So the area should be something like 1/25 + C? How come the +C disappears is what I'm trying to figure out.

[abdullah57habib]

How come we forget about the Constant (+C) when we find the anti derivative? So the area should be something like 1/25 + C.

Might be a stupid question mixed with confusion..

[chris642]

@abdullah57habib because this is a integral with limits, you only need +C when there are no limits involved, also known as an indefinite integral.

[jfhowlpendragon]

Officially my idol. Really. You're amazing. I had so much trouble over this for ages and now it all makes sense! :D

[zaxxx95]

Hey man...thanks for all these instructional videos...Really helped me out...

God Bless You!!! --- CheerzZz!!! ;-)

[hackereny]

Just amazing. One of the most helpful things that I've ever seen in internet. Keep posting more problems pls!



[hackereny]

Just amazing. One of the most helpful things that I've ever seen in internet. Keep posting more problems pls!

[hadjronaldogoal99]

Bro, I just want to give you the best hug ever. It's amazing to see that there are people willing to help confused uni students being taught by profs that can't even speak english, let alone being able to teach :$

I love you man.

[patrickJMT]

@hadjronaldogoal99 thank brother! this is such as easy way for me to give back that i would now feel bad if i did not do it : )

[hadjronaldogoal99]

Bro, I just want to give you the best hug ever. It's amazing to see that there are people willing to help confused uni students being taught by profs that can't even speak english, let alone being able to teach :$

I love you man.

[malicious6]

There really needs to be a math theorem that states that any math problem with 5's in it, should also never contain a variable, 's'. They just look way too much alike.

[sullivanseven]

Can you teach music as well?

[lasarikabab]

Wow - Austin TX is very very far from Sweden, but there is a Great Guy who help me with math - small world :-)

Thanks million!

[Osiyor]

Patrick, i was wondering if you can make a video on the comparison test for improper integrals... am sure it could have been used for this particular problem... Thank you

[crazypak11]

i think u messed up on the last step isnt the L'H rule suppose to be (t)/(1/e^-5t), not (t)/(e^5t)?

the in determinant product rule say f(X)g(x) = (f(x))/(1/g(x))

[VangY34311]

he's correct, what ur saying is pretty much the same thing.

[MCTeacup]

haha I was doing the exact same question in my text book when I decided to youtube improper integrals... and you give an example of the exact same question! Got stuck on the infinity * 0 issue... forgot about L'Hopital's rule! Thanks a bunch.

[nublered]

why doesnt he simpy say s*exp(-5s)=-d/(d5) exp(-5s) ?

[radiohead322]

aw YES. I was trying to do one exactly like this. and had no idea how to do it. THANKS.

[aStrimbu]

7:58 *facepalm* l'hospital

[rufinator007]

@aStrimbu shutup

[aStrimbu]

@rufinator007 how about we make love instead

[rufinator007]

@aStrimbu agreed, but i would prefer a money transfer as well.. paypal?

[electricfeel0]

I think you should change your name to Math God.

THANK YOU so much for making all these videos!!!

[kirarei12]

You are so fantastic. Thank you for putting these up with such a genuine intent of helping math students. You're a real gem!

[jsgacol]

Thanks for the video, It helped me heaps to solve a similar exercise I had. Thanks for taking the time making them and uploading them. =-)

[BnanaXD]

Is it really necessary to do L'Hospital? =.=

Just asking.....

[novatodeguitarra]

not actually when you turned it in (t)/e^(5t) you can say that it's zero for orders remember that polinomio logaritm ans exponential function "one beats the other" P/L=inf because polinomio has higher order E/P=inf P/E=0 L/P=0 L/E=0 and if you have polinomios only the one with the higher grade beats the one with the lower you can also do Taylor but in this case I prefer L'Hopital c'mos it's as simple as it cam be derive both numerator and denominator separatedly and check the new limit

[stbaby57]

Wow...your videos are AMAZING and so helpful! THANKS for taking the time to do them all!!!

[patrickJMT]

just trying to make the internets a place to go for some math help!

[tvcanthurtyou]

Awesome math problem! I have sweaty palms.

[patrickJMT]

hahahhahah

[Suckthebeef]

How come when you derive e^5t you get 5e^5t and the coefficiant of t doesn't change? I know it's probably a rookie quetion, but I'm still only an AS level student considering maths at university.

[DRodri90]

The coefficient doesn't change.

[scarface18707]

e^x is always e^x, doesnt matter if has a coefficent, but u would have to also do chain rule which would give u the number in front. ex: f(x)=e^9x, therefore f '(x)=9e^9x.

it will always drag the coefficient of the exponent.

[Bodacious1966]

Patrick, I'm just beside myself with your videos thus far. I returned to school to get my engineering degree after a 25 year hiatus. This type of tutoring wasn't even a thought back then.

I never had issues with math before, but when we got to improper integrals, I was stuck for some reason. I watched your video - sheesh nothing to it.

Currently we are examining the various testing techniques for convergence. I just scrolled down your list, and they are all there.

You are so great!

[patrickJMT]

hi bodacious!

glad to help.

if it makes you feel any better, this sort of video tutorials were also not available when i was a student.

now, as a lecturer/tutor, that is why i make them!

[Bodacious1966]

I'll tell you a funny story....my first class back, I ended up with a statistics professor who was YOUNGER than me.

THAT freeked me out, but he was an awesome teacher, and I miss him terribly. You remind me of him, in your methods and demeanor....and he is a genius (in my opinion).

Must be something with Math teachers. I fall in love with them too easy...hahah!!

[patrickJMT]

ahhaha! i was 22 when i first started teaching at university - was even thinner and younger looking then.  people did not think i was the one teaching the class! they thought i was a TA or something.

[Bodacious1966]

EXACTLY!!!

[RonaX]

dude thx for the explanation!!

really help me =)

[d3c4p3t4t0r]

f(x) = e^ax F(x) = (1/a)e^ax

[AtlantiXYL]

why E^-5t is NOT -00 ( -infinite)

[novatodeguitarra]

a^-b= 1/a^b

[Wampa181st]

thanks a lot I always wacth your videos after I learn something in class

[pollardrho06]

Nice

[cracknigga]

i love you, man, thanks!

this might even save my ass in the exam

never thought about looking for answers on youtube though

keep em coming, plz

[nayagam12]

Good job, At 9.04, i think it is not right to write one over infinity equals to zero, that means infinity multiply by zero is one!.

[Ren520]

i think u're wrong bro.

its limit is approaching 0, but u get the point.

[nayagam12]

You are doing a fantastic job.  But , what i am trying say is that at 9.04, you should omit the part, 1/infinity and just write limit 1/(5exp(5t) when t approaching infinity is zero. Coz, 1/infinity is undefined but the limit 1/(t) when t approaching infinity is zero.

[il3ftyi]

Nice job, very clear.

I never thought to look for help on calculus problems on youtube, next semester calculus 3 doesn't seem so scary now!

Keep them coming!

[tfou3lakmara]

great job

[patrickJMT]

thanks!

[vaccarovj]

at 8:50 it should be "the derivative of t (with respect to t of course)is one"

[ImbecilicMoron]

let me take time right now to congratualate you on ur precision! here, buddy, here's a Ph.d JUST FOR YOU!

[vaccarovj]

sarcasm is anger's ugly cousin. From now on, unacceptable.

[ImbecilicMoron]

rationalization is stupidity's inefficient survival tool.

ps: thanks for laying down the parameters of rhetorical devices. I'll try to be sincere next time.

[vaccarovj]

actually it was a quote from the movie "Anger Management"

great movie, very funny

[patrickJMT]

heheheh cant we all just get along (on the comments page of my random math videos)?

[ImbecilicMoron]

ooh! in that case, HAHAHAA

[vaccarovj]

what's your problem?

do me a favor. leave me alone please.

[patrickJMT]

hehehhe