# Integral of sin^2t*cos^4t

## Homework Statement

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

## The Attempt at a Solution

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

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The limits of the integral should be reversed.

Dick
Homework Helper

## Homework Statement

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

## 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
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

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

## 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) =   ?

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,

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