Find volume in (Int(Int(Int dx)dy)dz) form...

[xoninhas]

V = {(x, y, z ) ? R3 : x + y + 2z ? 1, x + y ? 2z ? 1, x ? 0, y ? 0}.

put the volume V in the form of:

\(\displaystyle \int\limits_{...}^{...} \int\limits_{...}^{...} \int\limits_{...}^{...} dxdydz\)

Is the result?:
\(\displaystyle \int\limits_{-1/2}^{0} \int\limits_{0}^{(1+2z)} \int\limits_{0}^{(-y-2z+1)} dxdydz + \int\limits_{0}^{1/2} \int\limits_{0}^{(1-2z)} \int\limits_{0}^{(-y+2z+1)} dxdydz\)


P.S.- Please mods and admins let me know if I'm pushing on the number of posts... :S

 

[tkhunny]

What are you doing? Please don't try to do things the hardest possible way.

Try this:

\(\displaystyle 2*\int_{0}^{1}\int_{0}^{1-x}\int_{0}^{\frac{1-x-y}{2}}\;dz\;dy\;dx\)

I assume you mean the little chunk cut off near the origin, rather than the unbounded pieces.