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Thread: Rotating the region y=x^2 and y=1 around y=6

  1. #1
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    Rotating the region y=x^2 and y=1 around y=6

    Hi all,

    I've been having difficulty with this problem.

    Rotate the region of y=x^2 and y=1 around the line y=6

    I have done it a couple times now and the homework website keeps saying that its wrong. I'm just looking to see if anyone sees an error in my work.

    So I would integrate pi(-6+x^2)^2 dx from -1 to 1. After working that all out I get 322pi/5 as my final answer. Just looking for some fact checking. Thanks!
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  2. #2
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    Re: Rotating the region y=x^2 and y=1 around y=6

    Using the method of washers and the graph's symmetry ...

    $\displaystyle 2\pi \int_0^1 (6-x^2)^2 - (6-1)^2 \, dx$

    ... try again.
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