Question

Evaluate the integral

Answer 1

\[\int\limits_{\frac{ -\pi }{4? }}^{\frac{ \pi }{ 4}} \frac{ t^4\tan t }{ 2 + \cos t}\]

Answer 2

Is there an identity I should use?

Answer 3

wait its oDD

Answer 4

symmetric at the origin! so 0!?

Answer 5

Try using Tan=Sin/Cos?

Answer 6

well since this is odd, you know that each area is going to cancel each other other because A - A = 0

Answer 7

Yeah definitely, you figured it out, awesome!

Answer 8

A quick check to see if something is odd is if you know that the other functions it's made up of are even or odd, we can do something like this: \[\Large \frac{ (-t)^4 \tan(-t)}{2+\cos(-t)} =-\frac{ t^4 \tan(t)}{2+\cos t}\] Since tan(-t)=-tan(t) we were able to show that for negative values of t it's exactly the same but opposite sign.

Answer 9

thanks for the tip!

Answer 10

Yeah, keep it up, I have been looking at your stuff the past couple days and you're really progressing.

Answer 11

thanks, I hope so haha