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Math Help - Finding the volume

  1. #1
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    Finding the volume

    Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.x = 5 + y2, x = 0, y = 1, y = 2

    I am unsure how to tackle this one.
    I tried rearranging the above equation to y^2=x-5 and the obtaining the necessary x values at the above y values, these were 9 and 6. So then i did the integral from 9 to 6 of pi multiplied by x-5 and this came out to be incorrect.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Finding the volume

    I always draw a sketch...this makes things clear...

    The volume of an arbitrary shell is given by:

    dV=2\pi y(y^2+5)\,dy

    Hence:

    V=2\pi\int_1^2 y^3+5y\,dy
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