Homework Help: Integral of sin^2t*cos^4t

1. Jan 27, 2012

skyturnred

1. The problem statement, all variables and given/known data

$\int^{0}_{pi}(sin^{2}t)*(cos^{4}t)$

2. Relevant equations

3. The attempt at a solution

I know you have to use trig identities.. but everything I try does not work.

2. Jan 27, 2012

skyturnred

The limits of the integral should be reversed.

3. Jan 27, 2012

Dick

You can do it with double angle identities. But you haven't shown anything you've tried yet. What did it occur to you to try?

4. Jan 27, 2012

SammyS

Staff Emeritus
$2\sin(\theta)\cos(\theta)=\sin(2\theta)$

So, sin2(θ)cos2(θ) =   ?

$2\cos^2(\theta)-1=\cos(2\theta)$

So, cos2(θ) =   ?

5. Jan 27, 2012

6.28318531

cos^2(t)=1-sin^2(t), then you use the double cos identity until you reduce it down to combination of cos(2t)'s,

Last edited: Jan 27, 2012