1. ## how to integrate?

$

\int_0^1 \int_0^{1-x} \int_y^1 \frac {\sin (z\pi)}{z(2-z)} dz dy dx

$

I first showed the function is integrable,
$
\lim_{ z\to 0} f(x.y.z)=\frac{\pi}{2}
$

and we know z will never be 2
so the function can be integrate.
How do I go on from here?

2. Maybe, if you switch the bounds of integration it will be a lot easier to integrate. Try to integrate z last and see what happens.

3. $z$ will never be $0$, either ...

4. Originally Posted by matheagle
Maybe, if you switch the bounds of integration it will be a lot easier to integrate. Try to integrate z last and see what happens.
I tried to do that, but how do I switch the bounds?