Explanation Formula used: cos 2 x = 1 + cos 2 x 2 Calculation: The integral ∫ − π 4 π 4 1 + cos 4 x d x rewritten as follows, Let cos 2 2 x = 1 + cos 4 x 2 Then 1 + cos 4 x = 2 cos 2 2 x . ∫ − π 4 π 4 1 + cos 4 x d x = 2 ∫ 0 π 4 1 + cos 4 x d x = 2 ∫ 0 π 4 2 cos 2 2 x d x = 2 2 ∫ 0 π 4 cos 2 x d x Let u = 2 x Then d u = 2 d x

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Chapter 8.3, Problem 58E

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To evaluate: The integral ∫−π4π41+cos4xdx.

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Chapter 8.3, Problem 57E

Chapter 8.3, Problem 59E

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