Calculus - Volume By Integration

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the y-axis:

y=(x-2)^3-2, x=0, y=25

Solve by either the disk or washer method.

I calculated the volume using the shell method and got 1250pi. However, I can't figure out how to calculate it using the disk method. The answers should be the same unless I calculated the volume using the shell method incorrectly.

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  1. I redid my shells because of a typo, and I got

    2π∫[0,5] x(25-((x-2)^3-2)) dx
    = 500π

    How did you get 1250π? What was your integral?
    We need to integrate over x, because the thickness of the shells is dx, not dy.

    As for discs,
    x = ∛(y+2) + 2

    v = π∫[-10,25] πx^2 dy
    = π∫[-10,25] (∛(y+2) + 1)^2 dy
    = 500π

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  2. I also checked my calculation in our previous post
    http://www.jiskha.com/display.cgi?id=1385311297

    I carelessly dropped the π in my last 3 lines, and should have used my calculator to add up the terms in my last line.
    My last line should have been 500π

    which then also agrees with Steve's new answer using shells

    So you have your two methods,
    mine using disks
    Steve's using shells
    both 500π

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