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Integration help please!

  1. Dec 4, 2005 #1
    Hi, I've got a few integration problems that I would like some help with:

    The one I'm currently working on is this:

    http://i26.photobucket.com/albums/c109/mathsnerd/4c37af04.jpg

    I'm supposed to change the order of integration but before I start integrating, I want to make sure I've changed the limits correctly. Can someone please check for me? Thank you! :smile:
     
  2. jcsd
  3. Dec 4, 2005 #2

    benorin

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    The bounds on the first integral read:

    [tex]0\leq x \leq 4 \mbox{ and } \sqrt{x}\leq y \leq 2[/tex]

    notice that y is bound below by [itex]\sqrt{x}[/itex]

    and so the integral you want has bounds:

    [tex]0\leq y \leq 2 \mbox{ and } 0\leq x \leq y^2[/tex]
     
  4. Dec 4, 2005 #3

    benorin

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    To be clear, the domain of integration is the smaller roughly triangular region in the upper left corner of the box [0,4]X[0,2].
     
  5. Dec 4, 2005 #4

    benorin

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    Afer changing the bounds, try applying the substitution

    [tex]u=x+y^2\Rightarrow du=dx \mbox{ so that }0\leq x \leq y^2 \Rightarrow y^2\leq u\leq 2y^2 [/tex]
     
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