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calculus

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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 - ,

    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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