   Chapter 6.1, Problem 41E ### 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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# Evaluating a Definite Integral In Exercises 39-46, use integration by parts to evaluate the definite integral. See Example 5. ∫ 0 1 ln   ( 1 + 2 x )   d x

To determine

To calculate: The value of definite integral 01ln(1+2x)dx.

Explanation

Given Information:

The provided definite integral is 01ln(1+2x)dx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

1ax+bdx=1aln(ax+b)

Calculation:

Consider the definite integral 01ln(1+2x)dx

Here,

dv=dx and u=ln(1+2x)

First find v,

dv=dxdv=dx

On further solving,

v=x …...…... (1)

Find du:

u=ln(1+2x)

Differentiate both side with respect x;

dudx=d(ln(1+2x))dxdudx=21+2x

And,

du=21+2xdx …...…..

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