The region W is the cone shown below.
The angle at the vertex is $\pi/3$, and the top is flat and at a height of $7\sqrt{3}$.
Write the limits of integration for $\int_W dV$ in the following coordinates (do not reduce the domain of integration by taking advantage of symmetry):
(a) Cartesian:
With $a = $ , $b = $ ,
$c = $ , $d = $ ,
$e = $ , and $f = $
Volume $= \int_a^b \int_c^d \int_e^f $ $d$ $d$ $d$
(b) Cylindrical:
With $a = $ , $b = $ ,
$c = $ , $d = $ ,
$e = $ , and $f = $
Volume $= \int_a^b \int_c^d \int_e^f $ $d$ $d$ $d$
(c) Spherical:
With $a = $ , $b = $ ,
$c = $ , $d = $ ,
$e = $ , and $f = $
Volume $= \int_a^b \int_c^d \int_e^f $ $d$ $d$ $d$
