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Math Help - Volume between two curves

  1. #1
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    Question Volume between two curves

    Hello, here is my question:
    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
    about
    So, I tired to solve it and I'm getting the wrong answer. Here is a graph:
    I did the integral of (1-x^6)-(x^6-5)dx from 0 to 1 and it wasn't right.

    Thanks,
    Matt
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  2. #2
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    I didn't see "pi" in the integral, did you leave it out of the answer as well?
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  3. #3
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    No, I did put it in for the answer, I forgot to put it in for the post...
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  4. #4
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    Okay, I think I almost got it, pi/int_0,1 (5-x^6)^2-16 dx I meant from 0 to 1 but I couldn't get the limits to work good in latex. I solved it and it still isn't the right answer.
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  5. #5
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    Is is not \pi\int_0^{1}\left[(5-x^6)^2-16\right]dx=\frac{696}{91}\pi?
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  6. #6
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    Yep, that's it, but I found out that I had to multiple the answer by two because it wanted the volume of the whole shape, so it includes -1 to 0 as well. I have a similar problem here:
    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

    about the y-axis.
    Would it be:
    \pi\int_2^{6}\left[\frac{1}{x^3}\right]^2dx=
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