Triple Integration, order reversal.

• Apr 6th 2008, 06:16 PM
Gotovina7
Triple Integration, order reversal.
I forget how to reverse the order of integration for triple integrals, here's the question.

Express the iterated integral

$\displaystyle \int_{-1}^{1} \int_{z^2}^1 \int_0^{1-y} g(x,y,z)dxdydz$

as an equivalent integral in which the y-integration is performed 1st, the z-integration second, and the x-integration last.

Thanks for any help.
• Apr 6th 2008, 07:55 PM
TwistedOne151
Limits of integration
The key is figuring out the limits of integration. Note that the region of space over which you are integrating is the region bound by the plane $\displaystyle x=0$, the plane $\displaystyle x+y=1$, and the parabolic cylinder $\displaystyle y=z^2$.

--Kevin C.
• Apr 7th 2008, 12:08 AM
Moo
Hello,

-1<x<1
zē<y<1
0<z<1-y

Just try to get some new inequations, for example 0<z<1 (this one is false, but you can try...)
• Apr 7th 2008, 08:56 AM
Mathstud28
It really helps
to get a visual so as that you can see exactly what you are dealing with