Posted by **Anonymous** on Wednesday, February 29, 2012 at 11:15am.

Find the volume when the area bounded by f(x) = xe^x, y = e, and the y-axis, is revolved around the y-axis.

- calculus -
**Steve**, Wednesday, February 29, 2012 at 12:57pm
xe^x = e when x = 1

using shells,

v = Int(2*pi*r*h dx)[0,.852]

where r = x

h = e-y = e - xe^x

v = 2pi*Int(x(e-xe^x) dx)

= 2pi *Int(ex - x^2 e^x) dx

= 2pi * (e/2 x^2 - e^x (x^2 - 2x + 2))[0,1]

= pi(4-e)

= 4.03

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