Posted by **DER23849** on Tuesday, January 24, 2012 at 9:44pm.

Use the shell method to find the volume of the solid generated by revolving the plane region about the line x = 9.

y = 7x − x2

y = 0

- calculus -
**Steve**, Wednesday, January 25, 2012 at 1:03pm
V = Int(2pi*r*h dx)[0,7]

where

r = 9-x

h = y

V = 2pi*Int((9-x)(7x-x^2)dx)[0,7]

= 2pi*Int(x^3 - 16x^2 + 63x)dx [0,7]

= 2pi(1/4 x^4 - 16/3 x^3 + 63/2 x^2)[0,7]

= 2pi(2401/4 - 5488/3 + 3087/2)

= 2pi * 3773/12

= 3773/6 pi

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