   Chapter 8.5, Problem 68E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# True or False? In Exercises 67 and 68, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. 4 ∫ sin x cos x   d x = − cos 2 x + c

To determine

Whether the provided statement “4sinxcosxdx=cos2x+C” is true or false.

Explanation

The provided integral is,

4sinxcosxdx=cos2x+C

Rewrite.

22sinxcosxdx=cos2x+C

Use the formula for 2sinxcosx=sin2x to simplify the above expression.

2sin2xdx=cos2x+C

Rewrite.

(sin2x)2dx=cos2x+C

Let u=2x.

Differentiate the above considered function.

du=2dx

Substitute u for 2x and du for 2dx

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