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Can you help me with this definite double integral?

  1. Oct 29, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm supposed to solve a definite double integral. It's supposed to be in the area of the triangle with vertexes at (0,0), (1,1),(0,2)

    2. Relevant equations
    integral of
    e^(y^2) * dy*dx

    3. The attempt at a solution
    First, I need to know the limits of x and y...
    So, that triangle is defined by the lines x=y, x=0 and y=-x+2
    with that I can define the limits for my integral

    (ps. I don't know how to use latex very well so this will look kind of weird, but whats on top is the upper limit and what is under that is the lower limit).

    I've tried it in the order [tex]\int[/tex][tex]\stackrel{1}{0}[/tex] [tex]\int[/tex][tex]\stackrel{-x+2}{x}[/tex] e^(y^2)*dy*dx
    and [tex]\int[/tex][tex]\stackrel{1}{0}[/tex] [tex]\int[/tex][tex]\stackrel{y}{0}[/tex] e^(y^2)*dx*dy + [tex]\int[/tex][tex]\stackrel{2}{1}[/tex] [tex]\int[/tex][tex]\stackrel{0}{2-y}[/tex] e^(y^2)*dx*dy
    But it both cases at some point I can't solve it. For example, in the second option I end up with an integral of 2*e^(y^2) and in the first option I can't even begin to solve that integral


    I have a test in a few hours so any help is much appreciated. Thanks
     
  2. jcsd
  3. Oct 29, 2009 #2

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    The limits on your very last integral are reversed, should be 0 to 2-y. You have the right idea about trying a dxdy integral, and the first one of the dx dy integrals works. You are correct the second one can't be worked. The problem might be miscopied or mis-stated such that the third point should have been (0,1), in which case you would have gotten it. Don't worry about it for the exam, you are good to go on that topic.
     
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