# Powers of Sines and CosinesEvaluate the | Ch 8.3 - 20E

## Problem 20E Chapter 8.3

Thomas' Calculus: Early Transcendentals | 13th Edition

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Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 20E

Powers of Sines and Cosines

Evaluate the integrals.

Step-by-Step Solution:

Step 1 of 6</p>

Here, we have to evaluate the given integral.

….(1)

Step 2 of 6

The given equation (1) can be written as .

Now, let us find the indefinite integral …..(2)

We know that  and .

Therefore, (2) becomes

.

….(3)

Step 3 of 6</p>

Consider

…..(4)

Let

Therefore, (4) becomes

Substituting back , we get

…..(5)

Step 4 of 6

Step 5 of 6

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Powers of Sines and CosinesEvaluate the | Ch 8.3 - 20E

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