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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 13.5, Problem 3E
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 3CP
Problem 4CP
Problem 5CP
Problem 6CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Evaluate the integrals in Problems 1-32. Identify the formula used.

3.   ∫ 1 4 d x x 9 − x 2

To determine

To calculate: The value of the integral ∫14dxx9+x2.

Explanation

Given Information:

The provided integral is ∫14dxx9+x2

Formula used:

For any variable u, the integral formula is,

∫duua2+u2=−1aln|a+a2+u2u|+C

Where, ‘a’ is not a function of u. and C is the constant of integration.

Logarithm property for any a, b,

lna−lnb = lnab

Calculation:

Consider the provided integral,

∫14dxx9+x2

The integral can be rewritten as:

∫14dxx32+x2

The denominator of the integral is similar to that of the denominator in the integral formula,

∫duu(au+b)

Therefore, the formula used is ∫duua2+u2=−1aln|a+a2+u2u|+C.

Now, use the formula ∫duua2+u2=−1aln|a+a2+u2u|+C, and compare from the integral ∫14dxx9+x2

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Chapter 13.5,
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