Integrals Resulting in Inverse Trigonometric Functions

From Department of Mathematics at UTSA
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Example 1

Evaluate the integral

Solution

Substitute . Then and we have

Applying the formula with we obtain

Example 2

Evaluate .

Solution

This integral requires two different methods to evaluate it. We get to those methods by splitting up the integral:

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The first integral is handled straightforward; the second integral is handled by substitution, with . We handle each separately.

: Set , so and . We have

Combining these together, we have

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