   Chapter 6, Problem 10TYS ### 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 − 1 x 2 + 49 x   d x

To determine

To calculate: The value of indefinite integral 31x2+49xdx.

Explanation

Given Information:

The integral is provided as:

31x2+49xdx

Formula used:

The formula 25 for integral u2+a2udu is:

u2+a2udu=u2+a2aln|a+u2+a2u|+C

General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Let u=x.

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

du=dx

Consider the provided integral:

31x2+49xdx

Rewrite.

31x2+49xdx=31x2+72xdx

Here, a=7, u=x and du=dx.

Substitute u for x, a for 7, and du for dx.

31x2+49xdx=31x2+72xdx

Use the formula 25 and solve the above integral as:

31x2+49xdx=[u2+a2aln|a+u2+a2u|]31

Substitute x for u, and 7 for a

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