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Integration question using Fubini's Theorem

  1. Aug 29, 2009 #1
    1. The problem statement, all variables and given/known data
    1 1
    ∫ ∫ e^x^2 dx dy
    0 y

    2. Relevant equations
    Fubini's Theorem:
    b g2(x) d h2(y)
    ∫∫ f(x,y) dA = ∫ ∫ f(x,y) dy dx = ∫ ∫ f(x,y) dx dy
    a g1(x) c h1(y)

    3. The attempt at a solution
    Hi everyone, it's not the integration that's causing me the problem here, it's the changing of the limits. I think my problem is that I can't visualise what it is I'm integrating. I'm not asking you to do the changing of limits for me, but could anyone please give me a clue as to what the shape looks like? I'm confused as to how the y can be variable (as in, how can you integrate from y to 1? What does it mean?).

  2. jcsd
  3. Aug 29, 2009 #2


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    Science Advisor
    Homework Helper

    For each fixed value of y between 0 and 1, you are integrating dx from y to 1. Does saying it in words help? So one of the boundaries of the region is the line y=x. The region of integration is a triangle.
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