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Math Help - Integrate with respect to x and y with a volume

  1. #1
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    Integrate with respect to x and y with a volume

    Let S be the surface defined by z= f(x,y) = 1 - y - x^2
    Let V be the volume of the 3-D region in the first octant bounded by S and the coordinate planes.

    Setup the iterated integrals for V in two ways:

    a) integrate first respect to x and then respect to y
    b) integrate first respect to y and then respect to x

    I dont know how to do this problem. I am completely lost.
    Thank you
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  2. #2
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    Re: Integrate with respect to x and y with a volume

    This is a pretty standard Calculus problem. If you were given it as home work you should have been given some instruction.

    One of the "coordinate plane boundaries" is z= 0. z= 1- y- x^2= 0 on the curve y= 1-  x^2 which goes from (0, 1) to (1, 0).
    So take x from 0 to 1 and, for each x, y from 0 to 1- x^2. And of course z goes from 0 up to 1- x^2.
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  3. #3
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    Re: Integrate with respect to x and y with a volume

    You left me scratching my head more than the problem itself.
    Im more confused than when i first started.

    Oh, i think its an iterated integral. So a triple integral. This is something we cover next week. I think i am a head of my self.
    Last edited by icelated; June 4th 2013 at 02:07 PM.
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