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Math Help - Finding volume using a double integral?

  1. #1
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    Finding volume using a double integral?

    Here is the question...

    Fine exactly the volume under the surface z=(1-x^2)(1-y^2) in the first octant.

    Can someone solve this and explain to me how to do it? The main thing I am confused about is how to find the limits. I know I am supposed to use the fact that it is in the first octant to find the limits, but I am not sure what to do with that information. Thanks in advance.
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  2. #2
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    Quote Originally Posted by Infernorage View Post
    Here is the question...

    Fine exactly the volume under the surface z=(1-x^2)(1-y^2) in the first octant.

    Can someone solve this and explain to me how to do it? The main thing I am confused about is how to find the limits. I know I am supposed to use the fact that it is in the first octant to find the limits, but I am not sure what to do with that information. Thanks in advance.
    What you need to know is when does the surface intersect the xy- plane in the first octant?

    Here is a hint to get you started.

    To find out set z=0 (why?)

    And solve

    0=(1-x^2)(1-y^2) for the values of x and y.

    Just use the zero product rule.

    Now sketch the region over you need to integrate. It turns out very nice.
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