   Chapter 7.7, Problem 39E

Chapter
Section
Textbook Problem

# Use Simpson’s Rule with n = 8 to estimate the volume of the solid obtained by rotating the region shown in the figure about (a) the x-axis and (b) the y-axis. To determine

To evaluate: To find the volume of the solid obtained by rotating the given region about

(a) x-axis (b) y-axis

By using Simpson’s rule with n=8

Explanation

Formula used:

(a) Volume of revolution about x-axis

abπr2dx

(b) Volume of revolution about y-axis

ab2πrh dy

(c) Simpson’s rule:

abfxdx=b-a3nfx0+4fx1+2fx2+4fx3..+4fxn-1)+fxn

b-an=h

Calculation:

(a) The volume of revolution about x-axis by Simpson’s rule

 x 2 3 4 5 6 7 8 9 10 f(x) 0 1.5 2 2.3 3 3.6 4 3.1 0 (f(x))2 0 2.25 4 5

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