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

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

#### Solutions

Chapter
Section ### 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,

lnalnb = 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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