# Evaluate the integral. {eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \sin^2 x \cos^2 x dx {/eq}

## Question:

Evaluate the integral.

{eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \sin^2 x \cos^2 x dx {/eq}

## Trigonometric Identities in Integrals:

One of the ways of evaluating integrals involving trigonometric functions is by implementing trigonometric identities.

Some of the trigonometric identities we can implement are:

{eq}2\sin(x) \cos(x) = \sin(2x) {/eq}

{eq}\sin^2(x) = \displaystyle \frac{1-\cos(2x)}{2} {/eq}

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First, we have to rewrite the integral by applying {eq}2\sin(x) \cos(x) = \sin(2x) {/eq} and {eq}\sin^2(x) = \displaystyle...