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Math Help - Help with integration using disks or shells

  1. #1
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    Help with integration using disks or shells

    I need help with this problem:

    Consider the region R, bounded by y=-4cos(x) and y=2.

    I can use either disks or shells to solve this problem.

    I need help setting up the integral required to find the volume of the solid obtained by revolving the region R about the line y=1.

    I think to set up this integral you would use this integral:


    2PI∫from 2 to 4 (x-1)(-4cos(x)) using

    shells.

    I'm not sure if I've set this integral up right.Have I done something wrong? Thanks in advance to all who can help,
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  2. #2
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    y = -4\cos{x} and y = 2 intersect at many places, forming many regions.

     -4\cos{x} = 2

     \cos{x} = -\frac{1}{2}

    x = 2k\pi \pm \frac{2\pi}{3} \, , \, k \in \mathbb{Z}

    which region are you looking at to rotate, specifically?
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