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.

Answer and Explanation: 1

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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...

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How to Use Trigonometric Substitution to Solve Integrals

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Chapter 13 / Lesson 12
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Trigonometric substitutions can be useful by plugging in a function of a variable, thus simplifying the calculation of an integral. Learn how to solve integrals using substitution, tables, by parts, and Riemann Sums through a variety of examples.


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