   Chapter 6.2, Problem 40E ### 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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# Using Integration Tables In Exercises 37– 44, use the integration table in Appendix C to evaluate the definite integral. See Example 4. ∫ 2 4 x 2 3 x − 5   d x

To determine

To calculate: The solution of definite integral 24x23x5dx.

Explanation

Given Information:

The provided definite integral is,

24x23x5dx

Formula used:

The formula for the integral u2a+budu is;

u2a+budu=1b3(bu2(2abu)a2ln|a+bu|)+C

The 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 expression:

24x23x5dx

Rewrite.

24x23x5dx=24x25+3xdx

Here, a=5, b=3, u=x and du=dx.

Substitute u for x, a for 5, b for 3, and du for dx. as;

24x23x5dx=24u2a+3udu

Use the above integration formula and solve the above integral as;

24x23x5dx=[1b3(bu2(2abu)a2ln|a+bu|)]24

Substitute x for u, 5 for a, and 3 for b

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