   Chapter 13.5, Problem 10E ### 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. ∫ 0 3 x 2 + 16   d x

To determine

To calculate: The value of the integral 03x2+16 dx.

Explanation

Given Information:

The provided integral is 03x2+16 dx

Formula used:

For any variable u, the integral formula is,

u2+a2du=12(uu2+a2+a2ln|u+u2+a2|)+C

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

For any a, b,

lnalnb = lnab

Calculation:

Consider the provided integral,

03x2+16 dx

The integral can be rewritten as:

03x2+42dx

The integral is similar to the integral formula,

u2+a2du

Therefore, the formula used is u2+a2du=12(uu2+a2+a2ln|u+u2+a2|)+C

Now, use the formula u2+a2du=12(uu2+a2+a2ln|u+u2+a2|)+C and compare from the provided integral 03x2+16 dx

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