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Math Help - Setting up integral to find the volume of a solid

  1. #1
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    Setting up integral to find the volume of a solid

    Find the volume of the solid in the first octant of xyz space, bounded below by the coordinate axes and the unit circle, and bounded above by z = 8xy.

    The unit circle would be x^2 + y^2 = 1.


    I know volume will be the double integral of 8xy.

    But I am having trouble setting up the limits of integration.

    Would the inner integral be from y = -sqrt(x^2 + y^2) to y = sqrt(x^2 + y^2)? then the outer one from 0 to 1 since we in the first octant?

    I am not liking the square root so i might be need polar i am not sure....
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  2. #2
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    I think my limits should actually be from 0 to 1 on the outer integral and from 0 to sqrt(1-x^2) on the inner integral is that correct?

    If i do that I am getting the answer to be 1/4

    My choices are A) 1/2 B) 1 C) 2 D) 4 E) 8 . So i must be doing something wrong.
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