Integration help please!

  • Thread starter elle
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  • #1
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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" [Broken]

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:
 
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  • #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]
 
  • #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].
 
  • #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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