I need to change the order of integration (without drawing the field) for:
$\int_{0}^{2}\int_{0}^{2z}\int_{y}^{2y}f(x,y,z)dxdydz$
to $\int\int\int f(x,y,z)dzdxdy$ and $\int\int\int f(x,y,z)dxdzdy$
I got to
$\int_{0}^{4}\int_{y}^{2y}\int_{\frac{x}{4}}^{2}f(x,y,z)dzdxdy$
and
$\int_{0}^{4}\int_{\frac{y}{2}}^{2}\int_{0}^{4z}f(x,y,z)dxdzdy$
which are incorrect apparently. What am I doing wrong? When it comes to the intervals, this is how I got to them:
$0 \leq z \leq 2$, $0 \leq y \leq 2z$, $y \leq x \leq 2y$, and so for the first integral:
$\frac{y}{4} \leq \frac{x}{4} \leq \frac{y}{2} \leq z \leq 2$, so $\frac{x}{4} \leq z \leq 2$
and for the second integral: $\frac{y}{2} \leq z \leq 2$, and $0 \leq y\leq x \leq 2y \leq 4z$ so $0 \leq x \leq 4z$