   Chapter 6.2, Problem 20QY ### 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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# In Exercises 16–21, use integration by parts or the integration table in Appendix C to evaluate the definite integral. ∫ x 3 1 x 2 9 − x 2   d x

To determine

To calculate: The value of definite integral 231x29x2dx.

Explanation

Given Information:

The provided definite integral is,

231x29x2dx

Formula used:

(1) The formula 34 for integral 1u2a2u2du is:

1u2a2u2du=a2u2a2u+C

(2) General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x.

Differentiate the considered function with respect to x using power rule of differentiation.

du=dx

Consider the provided integral:

231x29x2dx

Rewrite.

231x29x2dx=231x232x2dx

Substitute u for x, a for 3 and du for 6dx

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