[MOVED] Changing the Order of Integration

[Trenters4325]

What is the best way to do problems such as the following? Is it graphically? Algebraically?

Switch the dz and dy in the following integral:

\(\displaystyle \int\limits_0^1\, {\int\limits_0^{1 - x}\, {\int\limits_0^{1 - x - y}\, {dz\, dy\, dx} } }\)

 

[galactus]

You could rearrange it this way:

\(\displaystyle \L\\\int_{0}^{1}\;\ \int_{0}^{1-x}\;\ \int_{0}^{-z-x+1}dydzdx\)

 

[Trenters4325]

Thats what I'm trying to do. What is the best way to get that?

 

[galactus]

You're given z=1-x-y

Solve for y.