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Math Help - Volume of a solid rotated aroun the x axis

  1. #1
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    Volume of a solid rotated aroun the x axis

    R is the region in the first and second quadrants bounded above by the graph y=(20)/(1 + x^2) and below by the line y= 2. find the volume of the solid when generated by the x axis.

    Okay, so I set the hyperbola function as the outer radius and the horizontal line as the inner radius. Then I squared it and multipied by pi and integrated, but I'm getting a really big unreasonable number.
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  2. #2
    Junior Member eddie2042's Avatar
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    Quote Originally Posted by helpplz View Post
    R is the region in the first and second quadrants bounded above by the graph y=(20)/(1 + x^2) and below by the line y= 2. find the volume of the solid when generated by the x axis.

    Okay, so I set the hyperbola function as the outer radius and the horizontal line as the inner radius. Then I squared it and multipied by pi and integrated, but I'm getting a really big unreasonable number.
    I'm guess you did

    V = \pi\int\limits_{-3}^{3} (\frac{20}{1 + x^2} - 2)^2dx

    You're supposed to square each individual one like.

    V = \pi\int\limits_{-3}^{3} (\frac{20}{1 + x^2})^2 - {2}^2dx

    Even if you did that correctly, I got for my final answer

    V = 96\pi + 400arctan(3) \approx 1871.190104
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  3. #3
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    Ah, okay. But you don't think I set my integral up wrong? (As in, used to wrong inner/outer radii?)
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  4. #4
    Junior Member eddie2042's Avatar
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    Quote Originally Posted by helpplz View Post
    Ah, okay. But you don't think I set my integral up wrong? (As in, used to wrong inner/outer radii?)
    The truth is I don't know for sure how you set it up; you didn't explain too well.

    Yes, you are correct about setting the hyperbolic function as the outer radii and the y = 2 as the inner radii.

    But in the integrand, did you subtract them then square them?
    Or did you square each one individually then subtract them?

    Write it out..
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  5. #5
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    I subtracted and then squared. Which you explained was incorrect. Thanks for that. I was glad that my radii weren't wrong though, because that's my biggest struggle right now.
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