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

## Question:

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

## U-Substitution:

Replacing some functions from the original integral with a temporary substitute is one of the methods of solving definite or indefinite integrals.

This method is called the u-substitution. It is also called as the integration by substitution.

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U-substitution must be utilized to determine the value of the given definite integral.

Let

{eq}u = \cos x {/eq}

Then

{eq}\mathrm{d}u = -\sin x...