   Chapter 13.5, Problem 19E ### 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. ∫ 5 d x 4 − 9 x 2 x

To determine

To calculate: The value of integral 5dxx49x2.

Explanation

Given Information:

The provided integral is 5dxx49x2.

Formula used:

For any variable u, the integral formula is,

duua2u2=1aln|a+a2u2u|+C.

Calculation:

Consider the provided integral:

5dxx49x2

Multiply and divide by 3 and rewrite the provided integral as,

53dx3x4(3x)2

Now, the denominator of the provided integral matches with the denominator of the formula,

duua2u2

Therefore, the formula used for this integral is duua2u2=1aln|a+a2u2u|+C.

Now, use the formula duua2u2=1aln|a+a2u2u|+C and compare from the provided expression,

15dx3x49x2=duua2u2

In the provided expression, a=2

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#### Through (12,23), perpendicular to the line 4x 8y = 1

Single Variable Calculus: Early Transcendentals, Volume I 