   Chapter 5.4, Problem 4E ### 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. ∫ x a + b x d x = 2 15 b 2 ( 3 b x − 2 a ) ( a + b x ) 3 / 2 + C

To determine

To verify: The integral function using differentiation.

Explanation

Given information:

The integral function is xa+bxdx=215b2(3bx2a)(a+bx)32+C (1)

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.

Take the right hand function in Equation (1) and differentiate with respect to x.

ddx[215b2(3bx2a)(a+bx)32+C]=215b2[(3bx2a)32(a+bx)321+(a+bx)32(3b)]+0=215b2[(3bx2a)32(a+bx)12

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