# Use trigonometric substitution to evaluate the indefinite integral: {eq}\int \sqrt {25 - x^2} dx {/eq}

## Question:

Use trigonometric substitution to evaluate the indefinite integral:

{eq}\int \sqrt {25 - x^2} dx {/eq}

## Integrals:

The given indefinite integral can be solved by applying the direct formula for the given function from the integral calculus. But here we will make use of the substitution method to simplify the function first and then integrate it.

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{eq}\begin{align*} \ & \int \sqrt {25 - x^2} dx \end{align*} {/eq}

Put,

{eq}\begin{align*} \ & x = 5\sin t \end{align*} {/eq}

Differentiating...