Evalute the integral
∫
0
π
4
∫
0
π
2
∫
0
3
cos
(
ϕ
)
ρ
2
sin
(
ϕ
)
d
ρ
d
ϕ
d
θ
\displaystyle {\int_{{0}}^{{\frac{{\pi}}{{4}}}}}{\int_{{0}}^{{\frac{\pi}{{2}}}}}{\int_{{0}}^{{{3}{\cos{{\left(\phi\right)}}}}}}\rho^{{2}}{\sin{{\left(\phi\right)}}}\quad{d}\rho\ {d}\phi\ {d}\theta
∫
0
4
π
∫
0
2
π
∫
0
3
c
o
s
(
ϕ
)
ρ
2
sin
(
ϕ
)
d
ρ
d
ϕ
d
θ
using spherical coordinates.
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