How Do You Integrate sin^2(t)cos^4(t) from 0 to Pi?

[skyturnred]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

 

[skyturnred]

The limits of the integral should be reversed.

 

[Dick]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

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?

 

[SammyS]

Homework Statement

$\displaystyle \int_{0}^{\pi}(\sin^{2}t)*(\cos^{4}t)$ dt

Homework Equations

The Attempt at a Solution

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

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

So, sin²(θ)cos²(θ) =   ?  

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

So, cos²(θ) =   ?  

 

[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,