$z$

$z$

$r$

$r$

$1$

$1$

$0$

$0$

$1$

$1$

$0$

$0$

$2 \mathrm{\pi }$

$2\mathrm{\π}$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{FunctionAverage}\right]\left(\,z\=..\,r\=..\,\mathrm{\θ}\=..\,\mathrm{coordinates}\=\mathrm{cylindrical}\left[r\,\mathrm{\θ}\,z\right]\,\mathrm{output}\=\mathrm{integral}\right)$

$\frac{{\∫}_0^{2\mathrm{\π}}{\∫}_0^1{\∫}_r^{1}zr\ⅆz\ⅆr\ⅆ\mathrm{\θ}}{{\∫}_0^{2\mathrm{\π}}{\∫}_0^1{\∫}_r^{1}r\ⅆz\ⅆr\ⅆ\mathrm{\θ}}$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{FunctionAverage}\right]\left(\,z\=..\,r\=..\,\mathrm{\θ}\=..\,\mathrm{coordinates}\=\mathrm{cylindrical}\left[r\,\mathrm{\θ}\,z\right]\right)$

$\frac{3}{4}$