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Math Help - Confused of Volume of Solids(Washers Method)

  1. #1
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    Confused of Volume of Solids(Washers Method)

    Find the volume of the solid formed by revolving the region bounded by the graphs of y=1-x^3, x=-2, and y=1 about the line x=-2. Correctly write the integral, use calculator to solve. Answer:10.053

    So I solved the integral for dx and here is my integral.

    integral from 0 to -2 of (3-x^3)^2 x pi

    I keep on using the fnInt function, but I never got the answer(I've gotten 15.883)
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  2. #2
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    using disks ...

    y = 1 - x^3

    x^3 = 1 - y

    x = \sqrt[3]{1-y}

    R(y) = \sqrt[3]{1-y} - (-2) = \sqrt[3]{1-y}+2

    V = \pi \int_1^9 (\sqrt[3]{1-y}+2)^2 \, dy = 10.053


    using cylindrical shells ...

    V = 2\pi \int_{-2}^0 (x+2)(-x^3) \, dx = 10.053
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