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Math Help - Reverse order of integration

  1. #1
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    Reverse order of integration

    Compute the following by reversing the order of integration:

    \int_0^1\int_1^x xye^{y^4} dy dx

    Reversing the order, that's:
    \int_0^1\int_y^1 xye^{y^4} dx dy

    I got to a stage where I have:

    \frac{1}{2}\int_0^1 e^{y^4}(y-y^3) dy.
    Is that correct so far?

    I don't know if I can integrate this any further though... Any idea?
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  2. #2
    Moo
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    Hello,

    No, there is a slight problem.

    Because x\in[0,1]\Rightarrow x\leq 1
    And y is between 1 and x, which means that x\leq y\leq 1

    So 0\leq x\leq y\leq 1

    Hence we have :

    \int_0^1\int_1^x f(x,y) ~dydx=-\int_0^1\int_x^1 f(x,y) ~dydx=-\int_0^1\int_0^y f(x,y) ~dxdy

    that should be easier (and more correct) to deal with !



    P.S. : by the way, thank you very much, because in the three threads I've seen from you, you've always showed your work, and that's a very good thing
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  3. #3
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    Oops, heh. I was looking at the wrong region. Thanks!

    (PS. No problem re: the working. Thanks for noticing)
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