   Chapter 6.2, Problem 18QY ### 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. ∫ 0 8 x x + 8   d x

To determine

To calculate: The value of definite integral 08xx+8dx.

Explanation

Given Information:

The definite integral is,

08xx+8dx

Formula used:

(1) The formula 19 for integral ua+budu is:

ua+budu=2(2abu)3b2a+bu+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:

08xx+8dx

Rewrite.

08xx+8dx=08x8+(1)xdx

Here, a=8, b=1, u=x and du=dx.

Substitute u for x, a for 8, b for 1, and du for dx.

08xx+8dx=08ua+budu

Use the formula 19 and solve the above integral as:

08xx+8dx=[2(2abu)3b2a+bu]08

Substitute x for u, 8 for a, and 1 for b

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