   Chapter 5, Problem 26RE ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Evaluate the integral, if it exists. ∫ 1 10 x x 2 − 4 d x

To determine

The value of the integral function.

Explanation

Given information:

The integral function is 110xx24dx.

The region lies between x=1 and x=10.

Calculation:

Consider (x24) as u.

u=x24 (1)

Differentiate both sides of the Equation.

du=(2x)dx (2)

Rearrange Equation (2) to find the value of xdx as shown below:

xdx=12du (3)

Calculate the lower limit value of u using Equation (1).

Substitute 1 for x in Equation (1).

u=14=3

Calculate the upper limit value of u using Equation (1).

Substitute 10 for x in Equation (1).

u=1024=96

Substitute u for (x24) and 12du for xdx in the function as shown below:

110xx24dx=−<

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