   Chapter 5.4, Problem 2E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

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

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Verify by differentiation that the formula is correct. ∫ cos 2 x   d x = 1 2 x + 1 4 sin 2 x + C

To determine

To verify: That the given formula is correct using differentiation.

Explanation

Given:

The integral function is cos2xdx=12x+14sin2x+C (1)

Procedure used:

Verify the integral function using the procedure as follows:

• Differentiate the right side function with respect to x.
• Check whether the differential value matches with the left side function.
• If it matches, then the solution is correct, otherwise it is incorrect.

Calculation:

Take the right side function in equation (1) and differentiate with respect to x.

ddx[12x+14sin2x+C]=12+(14×cos2x×2)+0=12+12cos2x (2)

The mathematical expression for cosine function is shown below,

cos2x=1

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 