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Math Help - Help setting up integral using shells or washers

  1. #1
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    Help setting up integral using shells or washers

    I need help with the following problem:

    Suppose the region R is bounded by the curves y=2x + 1, y=2cos(2x),x=1, and x=3.

    In each part below, I need to set up the integral required to find the volume of the solid obtained by revolving the region R above about the indicated line. I can use either washers or shells, whichever is appropriate.

    a.) about the line y=-2
    b.) about the line x=-2

    For part a, I think you would set it up as ∫[from 1 to 3] Pi ((2x+1)+2)^2 - ((cos(2x))+2)^2 dx using washers.

    I am not really sure how you would go about setting up part b, but here is what I guessed you would do: ∫[from 1 to 7] Pi(3+2)^2 -(1+1)^2 dy using washers.

    Have I set either of these integrals up correctly? and if not I would appreciate any help explaining how you would go about setting them up correctly. Thanks in advance to anyone who can help me.
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  2. #2
    Eater of Worlds
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    You are correct about part a.

    part b would be, using shells:

    2{\pi}\int_{1}^{3}(x+2)((2x+1)-2cos(2x))dx
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