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Changing the order of a triple integration

  • Thread starter paraboloid
  • Start date
  • #1
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I'm given this definite integral:
[itex]\int_0^{1}\int_{\sqrt{x}}^{1}\int_{0}^{1-y}f(x,y,z)dzdydx[/itex]

I need to change the order to dydxdz, but I'm stuck trying to get the limits of integration wrt y.

24on636.png


[itex]\int_0^{1}\int_{x^2}^{0}\int_{}^{}f(x,y,z)dydzdx[/itex]

How do I find the limits of y?
 

Answers and Replies

  • #2
33,154
4,838
Just look at the original iterated integral to see the region over integration occurs.

z = 0 to z = 1 - y
y = sqrt(x) to y = 1
x = 0 to x = 1.

Sketch that region and it will help you determine the limits of integration for a different order of integration.
 

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