Trigonometric Integrals - Part 5 of 6

[breakdancer100]

great vid really helps. You should probably tell people that you forget to distribute the 1/2 though so they don't get confused.

[bestfriends1901]

What does m and n stand for? Please reply asap. Thanks for the vids! :)

[IndividualParties]

@bestfriends1901

They're just denoting arbitrary constants. In his example A=mx=2x so m=2, and B=nx=3x so n=3....

[smithsansoo]

second to the last line shouldn't the 1/2 distribute throughout? I got -1/10cos 5x + 1/2cos (-x). Great videos!

[McArthurDustloop]

@smithsansoo - yes i noticed that too, can someone confirm bout this? thanks btw mr patrickJMT !

[beautifulshapley]

I freakin hate the sergio ad. Its always the same boring add! It so annoying, why cant it be atleast different~! Anyways its worth waiting for the videos lol

[jlap1010]

I am watching this on my iPhone. Correct me if I am wrong. I believe u have forgot to multiply the 1/2 to 1/5. =]

[deco101]

i love how all 6 parts of this video is only 1 chapter of my test :(

[patrickJMT]

@Digidices just wait a few seconds

[cardioromano]

you teach way better than my professor.... i can barely understand him.. thank you for your awesome videos! they helped me a lot

[ashmeer12]

just had a question for the second question the answer at the end. Shouldn't it be -10 sin 5x+c cause u are using the distributive property of 1/2

[nykePF4]

yeah, 1/5 should be 1/10

[mosum91]

don't you have to multiply the 1/2 all way through to the entire integral so it would be 1/2 cos x - 1/10 cos x + C ?

[anupam15893]

I HATE MATHS AND ESPECIALLY CALCULUS NOW AFTER SEEING VIDEOS ON UR WEBSITE I HAVE BECOME CONFIDENT IN MATHS THANKS ALOT!!!!!!!!!!!!!!!

[mirandakoofficial]

i think you made a mistake in the answer.

shouldn't 1/2 multiply (1/5 cos x) to get the final answer as:

1/2 cos x - 1/10 cos x + c?

[spacioustee]

you are the best teacher ever. Thank you for all your videos.

[asmane73]

u deserve an international distinction in maths

[sikera182]

I got cos(x) in the first exercise instead cos(-x) and sin(x) in the second instead -sin(-x), but I guess it's ok since they have the same value, right?

[KimiWarrior]

for the last problem, can we just assume the cos (-x) to be cos (x) as it's an even trigo?

[KimiWarrior]

for the last problem, can we just assume the cos (-x) to be cos (x) as it's an even trigo?

[sprat87badoma]

For the last problem shouldn't the end have - 1/10 sin(5x) rather than -1/5 sin(5x)? As you have multiply the half from outside of the bracket.

[AntoineSarhan]

For the solution of the first problem, shouldn't the answer be: 1/2cos(x) - 1/5cos(5x) + C ?

Since cos(-x)=cos(x)

[shamzahm]

oops. its 1/10 not 1/5

the fact that i noticed proves you didnt bore me half to death like my teacher does :)

[imslave4u30]

@shamzahm thts true...there shld be 1/10.

[Balkance]

ugh. My teacher only spent 1 and 1/2 week on U Substitution. and went though the trigonometric integration in one day... never taught us the little side notes you had in the beginning... :(

[hybridindian]

Same here man. I wish Patrick was my professor.

[mrgoatsnake]

both times he forgets to distribute the 1/2 to the second term... I always forget to do this too haha

[lilmaqi]

@mrgoatsnake i noticed that too. i thought i had it wrong.

[chirrrs]

@mrgoatsnake i thought i was going crazy when my answer didnt add up both times! i guess its nice to know that we all tend to make the same mistakes! also, it helps to get to your own answer, and be convinced enough to doubt the given solution. he really should update it or put a note, though!

[ZhangyXD]

you should replace my professor

[syriankid4ever]

Thanks keep it up.

[yaguang]

Not sure if this was asked before, but could all those kind of integrals be integrated by integration by parts?

[tb9usa]

thanks man keep it up

[GelzBelz]

for both ending of each problem its supposed to be 1/10 since u open up the brackets. not 1/5

ur still great :D thanks man.

[igotdembombs]

Yea I noitced that too

[isoman2kx]

Hi Pat. Excellent video on this portion of Cal II.

Just a few comments that might improve it some. On your first formula you use M and N on the left side and then A and B on the right side. In the textbooks, they don't switch variables. I think it would be better to keep them consistent.

Also the annotation at 3:21 simply says "1/" it doesn't say "1/10"

Thanks again! :)

[SaMatta87]

I have a quiz tomorrow on Trigonometric Integrals and I finally understand how to do them thanks to your videos. I'm thinking about not even going to class anymore, in exception to days of quizes or exams, but rather watch your videos. Thanks a lot.

[calvinhobbesliker2]

couldn't you simplify at 3:40 by turning cos(-x) into cos x? they are the same, right?

[payasodundo17]

im kind of confused, didnt you have to multiply (1/2) to the integral of cos(5x)dx?

[saltlife85]

Awesome trig integral videos, best help ive had with it are these vids

[patrickJMT]

great, glad to help! : )

[saltlife85]

do you have vids on trig sub, or reihmann sums?

[patrickJMT]

yep, i have them both

[saltlife85]

awesome thanks

[avatarzero225]

I felt you rushed this a bit (something important to do perhaps?), and it showed at the end of the two problems because you didn't multiply by 1/2 for the second integrals. Besides this, you still did great. Thanks!!

[SWDanya]

OMG thank you so much for such wonderful videos from JMT. loving it all the way in London, uk

Just had my core 3 exam and now studying for core 4 and mechanics. These videos sure help!

[penkalli]

Hi, this video is posted on ur site under algebra section under the name "Graph Transformations - Horizontal and Vertical Stretching/Compressing is Discussed" , thanks, im going through all ur videos and learning alot

[patrickJMT]

ops! it sure is! thanks for letting me know! i will fix it

[Kryboc]

Hi Patrick. Should the second term be -1/10 sin(5x) because of the 1/2 out front? Thank-you for everything. Got an A- in Calculus 1 over the Summer and doing just as good in Calculus 2. Much happiness.

[patrickJMT]

ya! thanks for pointing out the mistake : ) i added annotations for it : )

congrats on the good grades!!!

[RockyBalboa211]

Hey man, thanks very much for this wonderful video, I am taking calculus 2 right now for my sophmore year at the university I go to, and we only had a day and a half to learn this material before the quiz and with the help of your videos, I believe I made a 92 or higher. The Definite trig intergral got me lol, I accidentally forgot to change my limits when I performed the sub. method... well once again thanks!!

[patrickJMT]

glad the videos helped!

[Waranle]

Thank you alot

[patrickJMT]

no worries! hopes it helps a bit