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Math Help - Triple Integration problem

  1. #1
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    Triple Integration problem

    I need to integrate x over the region bounded by x=1, y=1, z=1 and x+y+z=2. I am just wondering if the following limits are correct:

    1 < z < 2-x-y
    1 < y < 3-x
    1 < x < 2

    I get an answer of -9/8 so I'm assuming that's not right.
    Last edited by BrownianMan; September 24th 2011 at 04:34 PM.
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  2. #2
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    Re: Triple Integration problem

    It's been a while but I think the limits are as follows:

    1\leq z\leq 2-x-y
    1-x\leq y \leq 1
    0 \leq x \leq 1

    See once we have the limits for z, we can plug z=1 into our equation, solve for y and plot y=1, x=1, y=1-x in the xy plane and see the region clearly to determine the limits for x and y

    So we get y=1-x and when we plot it we can see that its the lower limit for y
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  3. #3
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    Re: Triple Integration problem

    I get -1/8 using those limits. Does it make sense for the answer to be negative?
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  4. #4
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    Re: Triple Integration problem

    well with my limits you should have gotten -1/6, but yeah this answer should be positive so something is wrong
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  5. #5
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    Re: Triple Integration problem

    Alright if you reverse my top and bottom limits on z then I think we're good. We both made the mistake of assuming that the region of integration was bounded above by the plane given by x+y+z=2, but that plane is actually the bottom of the region
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  6. #6
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    Re: Triple Integration problem

    Ok. I get 1/8 now. Matlab gives the same answer. Looks right.
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