Trigonometric Integrals - Part 1 of 6

[Hewicks]

couldn't this be done in 4 steps? Good video though :)

[AndrewMon2008]

you sir, are a Hero



[Angelgrrl04]

You should move to New York and teach at my college :3

[patrickJMT]

@Angelgrrl04 too cold :)

[assassin465]

Why does my teacher tell me not to use u substitution for trancendental functions?

[sskipe109]

Thank you man, I'm gonna get an A in Calc 2 thanks to you. Where can I donate??

[patrickJMT]

@sskipe109 if you click a video link on my website, a donation link pops up : )

[supersal001]

@patrickJMT he won't donate.... just saying.

[patrickJMT]

@supersal001 yes, i know :) i think about 0.0001% do. literally.

[supersal001]

@patrickJMT 0.0001%? thats better than being the 1%!! Just donated, for real. I am the 0.0001%. Occupy Me.

[patrickJMT]

@supersal001 thanks :)

[ILoveCristianoR]

Hi, I have a question about the second example, if you take u=cos(x), would the answer be:

-(cosx^4)/4 + (cosx^6)/6 ??

[tRGodzApostle]

this is the hardest part of calc 2 imo

[muktipanchal]

thank you!!!!

[MultiMetalBender]

hmmmm.... a little bit correction to the 2nd example... the answer should be 1/4sin^4x - 1/7sin^7x right???

:)))

[Godbornadam]

@MultiMetalBender No, he is right. When he distributes U^3(1-u^2), you must remember that when multiplying exponents of the same base, their quantities ADD, they do not get actually get multiplied. For example, U^5(U^6) = U^11, not U^30....then take the anti-derivative.

[honeypot11]

this part of math keeps cropping up and i keep forgetting it -sigh-

[GgGXxX93]

Thanks a lot !

Tmrw's Calculus1 exam should be a piece of cake for me now !

[mangaliewa]

i still dont get how someone can freaking dislike something that is free and education.



[Mallari1]

I've learned more than my professor in which I pay $700/credit hour. And this is free! The wonders...

[patrickJMT]

@Mallari1 yep, youtube is a nice place when nice people post nice stuff ; )

[lazarus343]

for your second example, I broke up the sinx again just to see what happened. I used cosx for u like in your first example and I got your final answer except the signs were reversed. What did I do wrong?

[ejrsfnm4]

Received a 92% on the calculus II test.  I went from D's to A's since iv'e been watching your tutorials. Thanks man!

[patrickJMT]

@ejrsfnm4 that is great! keep up the hard work!!

[FenixEven]

I clicked the ad (even though it was a mormon ad with no application to me) just so I could give even a little bit back for what you just gave me.

[patrickJMT]

@FenixEven : )

[MrKenken2121]

@patrickJMT are you an engineering teacher?

[Gazzawey]

u cant imagine how thankful I'm for this series thanks a lot sir please keep post more videos and examples u r my only source of teaching calculas

[patrickJMT]

@Gazzawey i will keep posting, just for you : )

[xxcowslayerxxx]

isn't there a way to do problems where you have sinx to a high even power or cosx with a high even power without using the reduction formula? im pretty sure my cal2 teacher showed us but i cant find any vids anywhere

[UNSCR1PTED]

Thanks for the help man. Question though, on example number two, if one was to choose to bust up (sin^3 x) instead, one would get a different answer right? I got (cos^6 x / 6) - (cos^4 x / 4) + C. Is that correct also?

[icha1992]

@UNSCR1PTED  yea i did the same thing also. is it still correct?

[solution91]

My tamu professor burns through this stuff, which makes it hard to follow. Being able to follow these vids at a slower pace really helps. Thanks as always patrick, your videos have been helping me for over a year now.

[patrickJMT]

@solution91 nice to know that i have been helping you out for that long : )

[atlboy72]

Thank God you made a youtube channel to make Calculus seem easier!. (and you help me pass calculus 1 and now help me with calculus 2)

[nickmagoo3]

For the last integral sin^3xCos^3xdx, Could you break down the Sin^3x and still have it correct? The difference only being it would have a negative and the constant would be different?

[Upupy]

Thank you mate.

[Pocket2011]

what if there's a number in front of the x (i.e sin^3 3x)?

[patrickJMT]

@Pocket2011 well, you can do a u-sub with u=3x and then proceed as normal

[just1guy93]

thank you thank you (= i've suggested your videos to at least 3 of my friends now, all in calc AB, as i used your videos to help myself when i took calc AB (= THANK YOU SO MUCH!

[laurrieee]

thanks for all the help. your videos are great. p.s just letting you know unfortunately for trigonometric integrals all the way to improper integrals teachers are not letting us use reduction formulas so I can only follow you so far. Unfortunately books do not show it either. I think i figured it out now but was confused at first. Just giving a heads up! Thanks again.

[RanyaI12]

Hello! first of all i'd like to thank you for these videos! they're awesome and extremely helpful! And second I have a question concernign the first example. Why did you turn out to be cosx?

[Szeania08]

Thanks, this really helps. :)

[weatherallc05]

it helps to be able to derive identities, just like the origins of words in english. at first i hated integration by substitution but i can see now that it saves alot of time especially with the nasty trig functions

[alexr1212]

wow it is awesome how clear this is. You make calculus easy to understand. thanks!!

[sofiakafairyS]

this video helped me a lot! thnx :)

[aligh18]

yes, because nerds watch x-men

[lobsidedballs]

wow you explain it 10x better than my book (Calculus Early transcendental functions: Larson Edwards) because they multiply cos2x to the trig and the split it into two i was confused how they did that until you showed the u substitution procedure (my book skip that part) This book sucks in explaining.

Thanks man!!!!

[zdfer]

Partick YOU are AWESOME! thanx a ton! i wld have flunked my math exams if u wldnt have made all this videos!

[greyphantomXIII]

i understand a lot...

more clear than what i studied before..

thanks for that...

[greyphantomXIII]

i understand a lot...

more clear than before..

thanks for that...

[greyphantomXIII]

i understand a lot... thanks for that...

[RickyPedia02]

hmm so you take du out and treat it just as you treat dx at the end of equations, meaning with respect to x? why do we put dx, or in this case du, on the end of equations? by the way i love your videos you're an incredible teacher :)

[mp3859]

shouldn;'t it be u to the power 7 over 7 instead of 6?

[fafase]

@mp3859 a^m times a^n =a^(m+n) so u^3+2=5 then u^6 over 6

You thought of (a^m)^n which is a^m times n.

hope that helps.

[ianIsMath]

it seems that your answer to the first example was not multiplied by -1, because before you arrived to the final answer, you factored out -1, so if we are going i=to integrate that, the answer must be the whole expression integrated times the -1 which was factored out earlier in the solution.

[peppers1616]

i fucking hate to have to memorize stuff.... it sucks!!

[patrickJMT]

@peppers1616 so learn to derive them. no one remembers all this stuff.

[peppers1616]

@patrickJMT i mean the trigonometric stuff... like sin(A+B) and stuff like that

[Ghaiyst]

@patrickJMT But I believe that it's harder to remember the processes involved in getting a trig. identity than to remember the actual identity. I figure you either have a knack for remembering formulas, or use natural genius talents to crack out amazing processes involved in getting the identities. So, for me, once I memorize an equation, it gets easier to remember the process of getting it. My mind works in odd ways, but I like it! :) BTW, thanks for all your videos! Im brushing up on old stuff

[iBankai7]

what if you found it in terms of cosx for the last part? and turned sin3x into cos's would that be right too? how do i know which one to do?

[beereaters]

@iBankai7 Any integral is path independent if it is a continuous function (which Sin and Cos are) so where you start does not matter. You can break up either the Sin or the Cos. But better than asking, use what this video shows and try it both ways and see if (and you should) get the same answer. Then you can try other functions like Tan and Cot and see what happens. you'll start to notice some patterns and that's when this kind of math becomes REALLY REALLY fun. Sudoku just can't compete. :)

[d1ckyj0nes]

Swell

[griffithsqwerty]

hi is this is university or high school level maths? thnx

[patrickJMT]

@griffithsqwerty it suppose it depends on if you take it in high school or at the university.  well prepared high schoolers can easily take calc 2 and beyond

[Sasasaam]

@patrickJMT Yah. I'm actually a Freshman, and I've been trying to teach myself Calculus. Not as hard as it's made out to be...

But you get the point.

[inFraZor1]

Hey Patrick, great video... thanks a lot...

I have 1 question...

in the second example, i subsituted u = cos x and the final aswer i got was

-cos^4/4 + cos^6/6 + C

can u tell me what i did wrong?

[SonOfNye]

@inFraZor1 You didn't necessarily do anything wrong, the antiderivative could be different depending on which way you went with the trig identity. Had you split the sin(x) term up and swapped the squared term for (1-cos^2(x)) and then used u=cos(x), the answer will have cos in lieu of sin.

[inFraZor1]

@SonOfNye hmm... yeah thanks

i always imagined that any function would have only 1 integral... but i guess the "C" constant could be different for my answer... but even then, does this mean i have to add or subtract a pi/2 to equal my answer to the actual one?

[SonOfNye]

@inFraZor1 Well, the integrals are still technically the same, similar to the say that (1/x) is the same as saying (x^-1) both functions are telling you the same things, the information is just presented a little differently.

[querpa]

Thanks, I learned in 6 minutes what took my professor 30 minutes to teach.

[mysteryimpt]

hi I have a simple question you know how you mentioned sinx + cosx =1? but then in this question the sinx and cosx is bring multiplied right:S?sry a little confused. Thanks

[bgoas3]

if only i could pay you the amount i pay for my college calc course....you teach me more than my professor does....

[beststuff17]

Thank you, awesome. I would like to see more complicate stuff regarding sec square x dx, or tan^6x dx

[schmittcle12]

dude for real, spend 20 bucks pick up a real MICROPHONE. It sounds like we are in 1950 on the beaches of iwogima.

[patrickJMT]

@schmittcle12 hey GABE, try not to be such a douche bag, although with a name like GABE, it is probably pretty hard to not to be...

[cendrizzi]

@patrickJMT Agreed, you realize he spent his time to create these and they are free to use right?

Overall very good. Thanks for your help. I find that I do best by following along with a white board and stop the videos and try and to them and then watch your solution and see if I did it as expected (if not it works nicely to do them again).

[bigpotatofive]

@patrickJMT

No need to make fun of names. My name is Gabe too and I appreciate the help.

[GunnerTHB]

@patrickJMT Hey now not all Gabe's are douchebags. You owe me private math tutoring now haha j/k :)

[dvermilion]

@patrickJMT is that a cheap shot at valve developer gabe newell? if so, bravo.

[MVPSuns13]

@patrickJMT

Thanks man. People really don't understand that students have to pay big bucks to learn the same stuff you  teach you gift to the world. I just wanna say i appreciate it.

[waynickrd]

@schmittcle12 "dude". You should have spent your 20 bucks on a history book. its "Iwo Jima" moron! Also, the battle on the beaches of Iwo Jima was in 1945, not 1950.

[kevineugenius]

@schmittcle12 Spelling things wrong in an insult makes you look super awesome. Iwo Jima. Moron.

[rhall4th]

@schmittcle12 Iwo Jima was invaded in 1945 douche.

[cylixdemas]

@schmittcle12 Hey! Be grateful! This guy helped me pass Calc 2

[fingerboy18]

@schmittcle12 Yeah it's because the mic is in your asshole.

[Hockeysktr17]

I <3 PatrickJMT (no homo).

You're the man 

[Trustpt]

Love your videos patrickJMT, but damn those youtube ads.

[FallenAngel2611992]

FUCK MATH !!

[Zadamanim]

@FallenAngel2611992 you be trollin

[patrickJMT]

@FallenAngel2611992 you tell that math.

[pty1717]

@FallenAngel2611992 You said it.

[gagikRLHS]

I love calculus

[OddRobb]

Does knowledge of trig identities make u sexier

[patrickJMT]

@OddRobb yes

[Ayplus]

@patrickJMT R u sure for the last example it doesnt matter which you use. When I used cosine, the answer was different, it was negative and cosines replaced sines

[beereaters]

@Ayplus Make sure you check your arithmetic!!! Algebra is seriously the hardest part of all these math classes because it is still SO easy to miss a negative or something simple because you can overlook the details trying to get your head around the big picture. It's like missing a tree when you look into the forrest... (It sounds like you are on the right track at least, see if you can find you're error, the - should cancel in the end)

[icha1992]

@patrickJMT what about the cosine replacing the sine i got in example 2? i try to do the example 2 w/o looking at ur videos after watching the first one, n i got (-cos^4)/4 + (cos^6)/6 + C

[inFraZor1]

@OddRobb only if you got patrick's brain

[Aviel31]

I wish you could take my calculus final for me tomorrow :(

[lllBOLTlll]

saw the video answered ? for me thx lol

[lllBOLTlll]

wat happens if you have two odd man outs like sin^3cos^3

[alexoftennis]

Hi. For the second example would you get the same answer if you chose to split the sin^3x instead of the cos^3x? So is the answer (-cos^4x)/4 + (cos^6x)/6 + C the same as the answer you got?

[Joesire]

Thank you for this. I was needing this.

[mhaeyah07]

what would be the determining factor of labeling them as u and v?

[alonsan100]

you lost me at 3:07

[alonsan100]

dangg.. you lost me after 3:15..

[Ndlovukazee]

You are the best!!!

[Lulrage]

Thank you so much for making these videos. I've had the same Cal I and II teacher the past two semesters and he is a very good teacher he just likes to spend a lot of time explaining the theorems and proving them and it leaves very little time to see examples being done. Your videos are always a huge help to come look back on after class.

[BESTOFBOND007]

do you have videos of probability?

[BESTOFBOND007]

hey...cant we do these using multiple angle formulae....atleast some of them?

[jacoman1234567]

I'm having trouble integrating root (1-x^2)dx, could anyone help me please?

[patrickJMT]

@jacoman1234567 ops, misread that. you would use a trig substitution; x = siny

[jacoman1234567]

@patrickJMT Ah I see it, so you'll 1-sin(y)^2 under the root, which becomes the root of cosine squared, thanks a million, you truly are a lifesaver :D

[BESTOFBOND007]

@jacoman1234567 dude,you had better learn all trig formulae before this....conversions will be damn easy

[xXElvisguyXx]

silly trig functions just hangin out...

[karibmar]

You should move to Puerto Rico and become my professor. Thank you for saving my life and career! =)

[patplayer92]

Thanks man this stuff saved my math average.

[kinghandles718]

couldn't you have used the shortcut method if u had distributed the cosine, thus getting:

[ cos^2(x) - cos^4(x) ] sin(x)

derivative of sin is in the problem, so raise the powers of cos by one and divide by new power right?

although im guessin you wanted to demonstrate proper u substitution... lol im gettin ahead of myself

[eoterm]

Man these videos are a life saver! Do you have any videos where you do Integration of rational functions where you have to do a long division and partial fraction decomposition, or integrals of stuff over things like atan(theta) where you have to draw a triangles, in some books it comes after these type of trig integrals

[laker1032]

@ Patrick, When I first changed to an Economics major last year I didnt know if I could climb the huge mountain of math. I took 6 classes in a year, starting from elementary algebra to calculus 1, I am now taking calculus 2 and I could say that with your help I have been able to ace my classes. I can now face the subject which I have feared for years and hold my head up high! Thank you for all of your help!! U rock!! Ur helping people overcome their fear of math!!

[eunkuk91]

is it still possible to sub cos^2x instead of the sin?

if no can u plz explain why...

btw ur vid is so much better than my teacher...

[viktorgoa]

Patrick, last year i did a foundation programme, 4 maths modules in it. With the help of your videos i got straight A-s :). Thank you!

[patrickJMT]

@viktorgoa congrats, that is very good!

[bartmonkey13]

@patrickJMT so I hear you got straight A's in a foundation program with 4 math modules in it, good job!

[datHulkinZ]

thanks man

[EatShanklish]

Thank you again Patrick, saved me. Question though, If both sin and cos are raised to an odd power, shouldn't we bust both of them? Like it would be:

S (sin^2)(sin)(cos^2)(cos) ?

[patrickJMT]

@EatShanklish no, you can just pick one

[Tigerjz32]

dang man, nice vid but idk if they will ask this hard questions on tests

[drwhoandphysics]

!QUESTION!!!: I thought that the "dx" in "S f(x) dx." was just notation. I thought that it just indicated that the function is being integrated in terms of "x." But in the video, it is treated as an actual variable. Somebody, please explain.

[shinril]

what case is this? cos^64xdx? when i had this problem i used the 2nd case and somehow i got the odd fraction in the end. :( i know its wrong. i need help patrick. could you please help me on this?

[renatinhaturri]

you really are saving my graduation. I recommend your videos to

all my friends here in Brazil. Thank you very much!!!

[kakarott008]

thank you SIR Patrick

[ralfviktor11]

thank you SIR patrick. you are a blessing.

[SeanRVCA]

thank you soo much for all your help ... you helped me get through calculus 1 with your videos, and now you're helping me understand calculus 2 .. you are a good man patrick

[chinamap]

this helped so much!

[andi039]

i hope you're as considerate as my teacher in teaching calculus.

[SJupiter01]

i hope you plan to teach high school but mainly college! Schools need good math teachers like yourself! (btw i'm going to be one too)

[d5ss]

dude you are Genious!!! didnt understand anything my lecturer taught and this made me realize that its not the subject but the teacher is SHIT!!!!! :D thanks!!

[Olumaintain900]

ur a total LEGEND mate

[Magicpotato]

THE ANSWER OF THE SECOND PROBLEM IS WRONG.

PLEASE CHANGE IT OR MAKE A NOTE. Thankyou.

Hopefully writing in caps got your attention.

[jonxeryus]

@Magicpotato

I agree with you buddy. For the second problem, He first says distribute the U^3 to the 1, then he ADDS the U^3 + U^2? Totally wrong, he was supposed to multiply them, being equal to U^6... Then you end up with U^4 / 4 - U^7 /7 + C, no?

[HappyVraal]

@jonxeryus Your wrong, your thinking of having your (u^3)^2 which would give you u^6, but you have to remember, when you multiply two variables you add their exponents, not multiply them, he has it right, it should be u^3-u^5 then he does their anti derivatives correctly, Try to remember back to your simpler algebra days!

[jonxeryus]

@HappyVraal RATS! Honest mistake buddy. Clearly, i need help in this area, hence why i am watching these videos. Thank you very much. I really do appreciate it.

[lhesther99]

@HappyVraal yea. the answer is right dude. just look for the law of exponents to brighten your mind guys. xD . x^m(x^n) = x^m+n.

[ferbanition]

Pretty sure that's not the right answer the - (sinx)^6/6 part of the answer should be: -(sinx)^7/7

the antiderivative of u^6 is U^7/7

[ferbanition]

nvm

[JarOfBuckeyes]

I feel foolish for spending thousands of dollars on calculus classes. All I need is a text book and this guy's videos.

[man122190]

the answer is different when i used cosine, some please clarify.

[Myounka]

@man122190 you got an equivalent answer. -cosx = sinx

[13loodLust]

The main point of this vid: Make one of the things odd so you have something for the du to cancel out.

[greenbookchannel]

nice video keep on posting " I PASS THE EXAM INTEGRAL CALCULUS" !!! thanks :))

[kojelja0]

very good and helpfull video, thank u a lot ^^

[hayley071092]

Will your answer be different if you chose cos instead of sin or sin instead of cos?

[man122190]

i tryed cosine and the answer is expressed in -cos4/4 -cos6/6 + C. which one is the answer anyone plz. these are the things that throw me off.

[pughyflyhalf]

why is it that when u=sinx that du=cosx dx? i though du=cosx

[rgrybra]

∫ cosx dx is the same as du=cosx dx, which equals sinx!

[pughyflyhalf]

in the last example, where does the cosx he took out come back into things, does he completely ignore it and integrate the rest because surely the extra cox^1x would make a difference to the overall answer??? help!!!

[andrewbellini]

For the first problem, instead of pulling the negative sign (from -du) outside the integral, wouldn't it be easier just to flip the (1 - cos^2) to (cos^2 - 1)?

[adavidmawk]

you cannot do that because the identity is sin^2+cos^2=1 therefore sin^2=1-cos^2.

1-cos^2 is not the same as cos^2-1

[robmon325]

thanks for the video man...test coming up soon this was real helpful!

[rfdavis09]

wow, this video was really helpful! I've been having a lot of trouble with college calculus and I wish it was this easy to understand in class. Thank you SO much for uploading these, they were awesome.

[autumnofmyheart]

I thought you said it doesn't matter what you choose to break up. So I chose to break up sin^3x. which forces to make u=cos x. then my final answer will be in cosine and not sine.

[hardkoreafg]

Very helpful video thanks