Chapter 5.2, Problem 42E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

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

To determine

To evaluate: The integral function using properties of integral.

Explanation

Given information:

The integral function is 0πsin4xdx=3π8.

Calculation:

Apply property of the definite integral

abf(x)dx=baf(x)dx (1)

Compare the integral the integral function with Equation (1) and obtain the values as follows:

f(x)=sin4xa=0 and b=π.

Substitute sin4x for f(x), 0 for a, and π for b in Equation (1).

abf(x)dx=baf(x)dx0πsin4xdx=π0sin4xdx

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