   Chapter 6.2, Problem 39E ### 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. ∫ 3 6 x 4 x − 7   d x

To determine

To calculate: The solution of definite integral 36x4x7dx.

Explanation

Given Information:

The provided definite integral is;

36x4x7dx

Formula used:

The formula for the integral ua+budu is:

ua+budu=1b2(bualn|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:

36x4x7dx

Rewrite.

36x4x7dx=36x7+4xdx

Here, a=7, b=4, u=x and du=dx.

Substitute u for x, a for 7, b for 4, and du for dx as;

36x4x7dx=05ua+budu

Now, use the above integration formula and solve the integral as:

36x4x7dx=[1b2(bualn|a+bu|)]36

Substitute x for u, 7 for a, and 4 for b as;

36x4x

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