Describe the iterated integral $\int_0^1\int_0^{1-(y-1)^2}\int_0^{2-x}f(x,y,z)dzdxdy$ both by algebraically and drawing.
That triple integral looks crazy for me.. how can I define a set that describe it. The only thing i know about the set is $x,y,z \ge 0$...
The region is a solid one which is bounded by the plane $z=0,z=2-x$ and a cylinder $x=1-(y-1)^2$ and $0\le y\le 1$: This can be shown by the solid red region below: