   Chapter 6, Problem 9TYS ### 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 8–10, use integration by parts or the integration table in Appendix C to evaluate the definite integral. ∫ 3 6 x x − 2   d x

To determine

To calculate: The value of definite integral 36xx2dx.

Explanation

Given Information:

The provided definite integral is,

36xx2dx

Formula used:

The formula 19 for integral ua+budu is:

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

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:

36xx2dx

Rewrite.

36xx2dx=36x(2)+(1)xdx

Here, a=2, b=1, u=x and du=dx.

Substitute u for x, a for 2, b for 1, and du for dx

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