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Math Help - Setting the limits on an integral for a joint pdf

  1. #1
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    Setting the limits on an integral for a joint pdf

    Hi everyone!

    I'm trying to solve a double integral to find the joint pdf of a function, but I'm not sure as to how to set the limits.

    f(x, y) = c(x^2 - y^2)e^{-x}<br />

    with  0 \leq x, -x \leq y \leq x

    I have to solve for the constant, c, so I thought that solving the double integral in the range of x and y and making that equal to 1 would solve for c, but I'm having trouble integrating. I suspect its my bounds for the integral.

    I'm not quite sure.... for my integration of the x values, I set the limits from 0 to infinity, and for the y values, the limits i set were from -x to x. Is that right?

    Many thanks!
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  2. #2
    MHF Contributor matheagle's Avatar
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    It seems to be 1=\int_0^{\infty}\int_{-x}^x f(x,y)dydx.
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  3. #3
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    Yeah, that's what I thought it would be as well. I just remember setting the limits to double integrals as being tricky for some odd reason... I felt unsure of myself.

    Thanks for the heads up, matheagle!
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  4. #4
    MHF Contributor matheagle's Avatar
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    You should always draw the region. You draw the lines y=x and y=-x.
    It is the region between those two in the first and fourth quadrants since x is nonnegative.
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