   Chapter 4.2, Problem 42E

Chapter
Section
Textbook Problem

# Given that ∫ 0 π sin 4 x   d x = 3 8 π , what is ∫ π 0 sin 4 θ   d θ ?

To determine

To evaluate:

The integral π0sin4θdθ

Explanation

1) Concept:

Use the property of the definite integral:

If a<b then  x=b - an  thus a - bn = -x

Therefore,

bafxdx=-abfxdx

2) Given:

0πsin4xdx=38π

3) Calculation:

By using the property of the definite integral:

The integral π0sin4θdθ can be written as

π0sin4

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