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Math Help - Volume of a Shape Under a Curve

  1. #1
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    Volume of a Shape Under a Curve

    Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves and about the y-axis.

    This is the graph:

    So pretty much I need to find the volume of the first quadrant rotated about the y-axis, giving me a sort of upside down, round nosed cone. I'm having trouble finding the radius to substitute into my equation of the area of the circle, which I want to integrate to find the volume. Any tips/ideas?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    you'll have to integrate wrt y

    invert to get x = f(y)

    x = sqrt(y) which is your radius

    V = integral(pi y dy) integrated from 0 to 4

    If you use shells(have you learned this methid yet?)
    then you don't have to invert

    you have 2pi integral(x*(4-x^2)dx)
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