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Math Help - volume of resulting solid

  1. #1
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    volume of resulting solid

    The region between the graphs of y=x^2 and y=4x is rotated around the line y=16.
    The volume of the resulting solid is

    i thought it would be the definite integral

    |16
    | pi[((x^2)^2)-((4x)^2)]dx
    |0

    but thats not right
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  2. #2
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    Quote Originally Posted by dat1611 View Post
    The region between the graphs of y=x^2 and y=4x is rotated around the line y=16.
    The volume of the resulting solid is

    i thought it would be the definite integral

    |16
    | pi[((x^2)^2)-((4x)^2)]dx
    |0

    but thats not right
    did you make a sketch?

    V = \pi \int_a^b [R(x)]^2 - [r(x)]^2 \, dx

    R(x) = 16-x^2<br />

    r(x) = 16-4x

    limits of integration are from a = 0 to b = 4
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