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Math Help - Can someone please just check my work here?

  1. #1
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    Can someone please just check my work here?

    Consider the region R in Quadrant I enclosed by the x-axis and y=-2x^2+4x.

    Consider V1, V2, and V3, formed by revolving R about y=4, y=-2, and x=4 resp. Compute these volumes.

    Here is what I got:

    For V1: use washers with outer radius 4 and inner radius 4-(-2x^2+4x). Do pi*integral (0 to 2) 4^2-(4-4x+2x^2)^2 dx, and I got 256*pi/15

    For V2: washers, outer of 2+(4x-2x^2), inner of 2. Do pi*integral (0 to 2) ((2+3x-2x^2)^2-4 dx, and I got 224*pi/15

    For V3: use shells, radius is 4-x and height is f(x). Do 2pi*integral (0 to 2) of (4-x)*(-2x^2+4x) dx, and I got 16*pi.

    Are these answers correct? Thanks.
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  2. #2
    MHF Contributor ebaines's Avatar
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    I think you have them all correct!
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