   Chapter 5.5, Problem 67E ### 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 definite integral. ∫ 1 2 x x − 1   d x

To determine

To evaluate: The definite integral.

Explanation

Given:

The definite integral function is 12xx1dx.

The region lies between x=1 and x=2.

Calculation:

Take the consideration as follows:

u=x1x=u+1 (1)

Differentiate both sides of the Equation (1).

du=dx

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

Substitute1for x in Equation (1).

u=11=0

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

Substitute 2for x in Equation (1).

u=21=1

The definite integral function is,

12xx1dx (2)

Apply lower and upper limits for u in Equation (2).

Substitute (u+1) for x, (x1) for u, and du for dx in Equation (2).

12xx1dx=01(u+1)udu=01(u+1)u12du=01(u1+12+u12)du=01(u32+u12)du (3)

Integrate Equation (3)

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Study Guide for Stewart's Multivariable Calculus, 8th 