   Chapter 5.2, Problem 35E ### 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 by interpreting it in terms of areas. ∫ − 1 2 ( 1 − x ) d x

To determine

To evaluate: The integral function 12(1x)dx by an area interpretation.

Explanation

Given information:

The integral function is 12(1x)dx.

The lower limit is x1=1 and upper limit is x2=2.

Calculation:

Consider f(x)=(1x).

Let consider y as function of x.

y=f(x) (1)

Substitute (1x) for f(x) in Equation (1)

y=1x (2)

Calculate the value of y1 using Equation (2).

Substitute 1 for x in Equation (2).

y1=1(1)=2

Calculate y2 using Equation (2).

Substitute 2 for x in Equation (2).

y2=1(2)=1

Therefore, the coordinates (x1,y1) is (1,2) and (x2,y2) is (2,1)

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Study Guide for Stewart's Multivariable Calculus, 8th 