calculus

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Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.
y = 6x
y = 18
x = 0

  • calculus -

    V = Int(2pi*r*h dx)[0,3]
    where
    r = x
    h = 18-y

    V = 2pi*Int(x*(18-6x) dx)[0,3]
    = 2pi * Int(18x - 6x^2 dx)[0,3]
    = 2pi*(9x^2 - 2x^3)[0,3]
    = 2pi*(27-18)
    = 18pi

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