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Math Help - Finding the volume of a solid using a double integral

  1. #1
    s7b
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    Finding the volume of a solid using a double integral

    Hi,I need help with the following;

    Find the volume of the solid cut from the first octant by the surface z=4-x^2-y

    I'm not sure how to set up the double integral. I'm also not sure even how to sketch this to determine the limits of integration. Are there steps I can follow to help sketch something like this?

    Thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by s7b View Post
    Hi,I need help with the following;

    Find the volume of the solid cut from the first octant by the surface z=4-x^2-y

    I'm not sure how to set up the double integral. I'm also not sure even how to sketch this to determine the limits of integration. Are there steps I can follow to help sketch something like this?

    Thanks
    start by graphing it in each plain.

    in the xy-plane, you have the curve y = 4 - x^2

    in the xz-plane, you have the curve z = 4 - x^2

    in the yz-plane, you have the curve z = 4 - y


    with the aid of a little sketch using these traces, and perhaps some minor calculations if needed, we find that the volume is given by

    V = \int_0^2 \int_0^{4 - x^2} z~dy~dx

    where z = 4 - x^2 - y
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