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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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.

4 6 2 x x 4 4 d x

To determine

To calculate: The value of definite integral 462xx44dx.

Explanation

Given Information:

The provided definite integral is,

462xx44dx

Formula used:

(1) The formula 21 for integral 1u2a2du is:

1u2a2du=12aln|uau+a|+C

(2) General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x2.

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

du=2xdx

Consider the provided integral:

462xx44dx

Rewrite.

462xx44dx=461(x2)2222xdx

Substitute u for x2, a for 2 and du for 2xdx.

462xx44dx=461u2a2du

Use the formula 21 and solve the above integral as:

462xx44dx=[12aln|uau+a|]46

Substitute x2 for u and 2 for a

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