# Change order of a triple integration

• April 5th 2010, 11:00 AM
squeeze101
Change order of a triple integration
I'm given this definite integral:
$\int_0^{1}\int_{\sqrt{x}}^{1}\int_{0}^{1-y}f(x,y,z)dzdydx$

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

http://i42.tinypic.com/24on636.png

$\int_0^{1}\int_{x^2}^{0}\int_{}^{}f(x,y,z)dydzdx$

How do I find the limits of y?
• April 6th 2010, 08:22 AM
hollywood
According to the integral, your region of integration is bounded by:

1. the plane z=0
2. the plane z=1-y
3. the surface y=sqrt(x), and
4. the plane x=0

(that means your diagram is wrong, though)

So I think the limits would be:
y from sqrt(x) to 1-z
z from 0 to 1-sqrt(x)
x from 0 to 1

- Hollywood