$D$ is the portion of the unit cylinder $x ^2 +y ^2 ≤ 1$ which lies between $z = 0$ and $z = 1$.
I normally solve questions like this by sketching the $z-r$ plane. Obviously I draw $z=0$ and $z=1$, but I am unsure how to sketch $x ^2 +y ^2 ≤ 1$. I know this can be written as $r^2 \leq 1$. But then this would mean I would be drawing $r \leq 1$ which would give a square with corners at $(0,0) (0,1) (1,1) (1,0)$. Is this correct?
For the bounds I know that since the domain is axysymmetric, then $0 \leq \theta \leq 2 \pi$. I can figure things out like $p \leq sec( \phi)$ and $p \leq cosec(\phi)$, but I really need to sketch the domain in the $z-r$ plane to figure out how to split the integral up.
I know there are other methods of solving but I only really understand by sketching in the $z-r$ plane if someone could please help?
$x^2 + y^2 = 1$ is the equation of a circle whose centre lies at the origin and which has a radius of one unit.
Essentially, $x^2 + y^2 \leq 1$ is the cross section of your cylinder, which lies between $z=0$ and $z=1$.
If you're having trouble sketch graphs of functions, you may use a graphing calculator, like Desmos, or GeoGebra.