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calculus 2

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Consider the solid obtained by rotating the region bounded by the given curves about the line x = -3.
y = x^2 , x = y^2

Find the volume V of this solid.
I keep finding the wrong answer.

  • calculus 2 - ,

    The two parabolas enclose an area between (0,0) and (1,1)
    y = x^2 or x=sqrt y is on the right and lower there.
    y = x^(1/2) or x = y^2 is above and left there. (All in quadrant one, no worry about signs )
    the radius to x = -3 is (3+x)
    so outer radius = 3 + sqrt y
    inner radius = 3 + y^2
    find outer volume
    pi (3+y^.5)^2 dy from 0 to 1
    find inner volume
    pi (3+y^2)^2 dy from 0 to 1
    subtract

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