   Chapter 8.1, Problem 85E

Chapter
Section
Textbook Problem

# Interpreting Integrals In Exercises 89 and 90, (a) sketch the region whose area is given by the integral, (b) sketch the solid whose volume is given by the integral when the disk method is used, and (c) sketch the solid whose volume is given by the integral when the shell method is used. (There is more than one correct answer for each part.) ∫ 0 2 2 π x 2   d x

(a)

To determine

To graph: The region whose area is given by the integral 022πx2dx.

Explanation

Given:

We are given with the integral 022πx2dx.

Graph:

The function to be integrated is y=2πx2. Area of a function y=f(x) is given by

A=abf(x)dx, provided f(x) is continuous in [a,b] and bounded by vertical lines x=a and x=b.

To sketch the region whose area is given by the integral 022πx2dx use TI-83 calculator as follows:

Step 1:

Open TI-83 calculator.

Step2:

Press Y= button

(b)

To determine

To graph: We use disk method to calculate the solid whose volume is given by the integral 022πx2dx.

(c)

To determine

To graph: We use shell method to find the volume of the solid given by the integral 022πx2dx.

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