# Evaluate the integral: {eq}\int_{0}^{\frac{\pi}{2}} \cos^3(\theta) \sin(2 \theta) \mathrm{d} \theta {/eq}.

## Question:

Evaluate the integral: {eq}\int_{0}^{\frac{\pi}{2}} \cos^3(\theta) \sin(2 \theta) \mathrm{d} \theta {/eq}.

## Definite Integral in Calculus:

There are many techniques to solve integral problems. To solve this problem we'll use u-substitution.

Next, we'll compute the boundaries to get the desired solution.

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We are given:

{eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \cos^3(\theta) \sin(2 \theta) \mathrm{d} \theta {/eq}

Compute the indefinite integral:

{e...