   Chapter 6.1, Problem 44E ### 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 12 x x + 4   d x

To determine

To calculate: The value of definite integral 012xx+4dx.

Explanation

Given Information:

The provided definite integral is 012xx+4dx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

(ax+b)ndx=1a(ax+b)n+1n+1,n1

Calculation:

Consider the definite integral 012xx+4dx

The above definite integral can be written as,

012xx+4dx=012x(x+4)12dx

Here,

dv=(x+4)12dx and u=x

First find v,

dv=(x+4)12dxdv=(x+4)12dx

On further solving,

v=2(x+4)12 …...…... (1)

Find du:

u=x

Differentiate both side with respect x;

dudx=d(x)dxdudx=1

And,

du=1dx …...…..

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