Which of the integrals are equal to
$$\int_{0}^{3}\int_{0}^{2}\int_{0}^{y} f(x,y,z) dz dy dx$$
a) $\int_{0}^{2}\int_{0}^{3}\int_{0}^{y} f(x,y,z) dz dy dx$
b) $\int_{0}^{3}\int_{0}^{2}\int_{0}^{y} f(x,y,z) dx dy dz$
c) $\int_{0}^{3}\int_{0}^{2}\int_{z}^{2} f(x,y,z) dy dz dx$
d) $\int_{0}^{3}\int_{0}^{2}\int_{0}^{z} f(x,y,z) dy dz dx$
I know that
$0\leq z\leq y$
$0\leq y \leq 2$
$0 \leq x \leq 3$
Putting it together I get $0\leq z \leq y \leq 2$ but I don't really know what to do from here.
Since I see that $z\leq y \leq 2$ I'm inclined to thing that the answers are (c) and (d)? Are both of them correct or is it either c) or d)?