   Chapter 5.2, Problem 37E ### 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. ∫ − 3 0 ( 1 + 9 − x 2 ) d x

To determine

To evaluate: The integral 30(1+9x2)dx by an area interpretation.

Explanation

Given information:

The integral function is 30(1+9x2)dx.

The lower limit is a=3 and upper limit is b=0.

Calculation:

The property of the integral is shown below:

ab[f(x)+g(x)]dx=abf(x)dx+abg(x)dx

Apply the integral property to the integral function.

30(1+9x2)dx=30(1)dx+30(9x2)dx

Consider f(x)=1 and g(x)=(9x2).

Consider y as function of x.

y=f(x) (1)

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

y=1

Hence, y1=1 and y2=1.

Therefore, the coordinates (x1,y1) is (3,1) and (x2,y2) is (0,1).

Consider y as function of x.

y=g(x) (2)

Substitute (9x2) for g(x) in Equation (2)

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Study Guide for Stewart's Multivariable Calculus, 8th 