Consider the set $W=\{(x,y,z)$:$x^2+y^2+z^{2}2,z1\}.$

$127$

GTIIT $-$ Winter $2024/2025$

Marco FARINATI

Infinitesimal Calculus $2$

$($a$)$ Describe $W$ in Cylindrical coordinates.

$($b$)$ If $f$:$WR,$ write ${}_{W}f$ as an iterated integral using cylindrical coordinates.

$($c$)$ Interchange the order of the integration drharrdz in the provious iterated integral.

$($d$)$ Compute the volume of $W.$