# 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