Trigonometric integrals - sin^mcos^n, m and n even (KristaKingMath)

Learn how to find the integral of the product of a higher order sine function and higher order cosine function. In this particular example, we'll talk about the method for finding the integral when sine and cosine are even

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[mayeboy]

Up late studying sin^2cos^4 and reading the work had me flabbergasted. Went to sleep, woke up & remembered my trusty online tutor. You absolutely rock. I watched this video and used your approach to solve mine with ease.

[baburo]

Holy cow! the blackboard and the chalk are as real as they get... thanks for the help, appreciate it.

[kristakingmath]

in that case you just go straight to the half angle substitution, and substitute (1/2-1/2cos(2t)) for sin^2t. then you just integrate term by term. make sure that when you take the integral of cos(2t), you use chain rule and divide by the derivative of the inside function, 2t. then evaluate at your limits of integration. :)

[kristakingmath]

yes, i'm planning to do a couple more of these. i would expect problem where m =/= n would be quite long and tedious. all of these problems usually are. unfortunately, the quickest way i know to solve them is still just to simplify the odd identity. :)

[lakshmi]

Excellent explanation... please post more video on math. Best math teacher. Good work. Thank you.

[mohammedalkhaldi]

You're my hero I can't thank you enough. If it was not for you, I would have failed

[mehtabahmed]

Simply perfect helped so so so so much.every video is phenomenal.

[Ensign_Cthulhu]

Sine and cosine terms come up a lot in e.g. electrical engineering when AC currents are being dealt with. So it's not improbable that if you're working in such a field you'll meet one.

[kristakingmath]

I'm referring to integrating this specific type of function, that is, a product of sine and cosine. :)

[MrBeanVR]

Your videos are excellent! You explain very well! Keep it up! :)

[holyshit]

I calculate it using Pythagorean identity and reduction formula (derived by parts with pythagorean identity)

[kristakingmath]

lol... ya didn't catch that until afterwards. :) btw, thanks for responding to jeremy0203 in the first place!

[israelheyrosa]

hi! can you do a video on how IBP was formulated? thanks!

[holyshit]

Rewrite trig function with sec(x) and tan(x) or cos(x) and sin(x)
From Euler substitution we will get
sec(x)=u-tan(x) for sec(x) and tan(x) version
or
cos(x)=(1-sin(x))u for cos(x) and sin(x) version

[ItsABettieRama]

what if the problem was just y= integral from 0 to x times (sin^2t)dt ?
would i just plug in the substitution? i'm so confused!

[karlroberts]

Did you get the (sinx)^2 = (1/2)(1-cos(2x)) from the sinxcosx = (1/2)sin2x on the left? or is it a seperate identity? Thanks v much x

[shardulkhadye]

What if m and n are different numbers ? We are left with (sinxcosx)^m(cosx)^n-m

[brslove]

i did this for sin^2(x)cos^4(x) and got stuck when i end up with (1-cos(4t))(cos^2(t)) I dont know how to remove the cos^2(t). I know I can use 1/2(1+cos2t) but that doesnt make it any simpler, since i end up with cos4t and cos2t multplying, can anyone explain?

[thy]

or you can use power reducing formulas.

[jeremy]

What real world use do these prolems have than being able to do them on say an exam.