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Math Help - Volumes

  1. #1
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    Question Volumes

    Find the volume of the solid formed when the region bounded by the parabola y = x^2 - 2 is rotated about (i) the X-axis (ii) the Y-axis.

    How exactly do I do this question? For the previous questions, there was a limit for both x and y but now...
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by xwrathbringerx View Post
    Find the volume of the solid formed when the region bounded by the parabola y = x^2 - 2 is rotated about (i) the X-axis (ii) the Y-axis.

    How exactly do I do this question? For the previous questions, there was a limit for both x and y but now...
    see this pic find where the curve intersect with the x-axis and the y-axis this is the limits you want y change from -2 to 0 and x from -\sqrt{2} to \sqrt{2}


    Volumes-exp.jpg
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by xwrathbringerx View Post
    Find the volume of the solid formed when the region bounded by the parabola y = x^2 - 2 is rotated about (i) the X-axis (ii) the Y-axis.

    How exactly do I do this question? For the previous questions, there was a limit for both x and y but now...

    For the first part since you are rotating around the x-axis you can find theh intercepts by setting y=0

    0=x^2-2 \iff x=\pm \sqrt{2}

    So your integral becomes

    \int_{-\sqrt{2}}^{\sqrt{2}}\pi (x^2-2)^2dx=2\pi\int_{0}^{\sqrt{2}}(x^2-2)^2dx=...

    Try something similar for the 2nd one.
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