Answer
$$27$$
Work Step by Step
$$\eqalign{
& \int_{ - 1}^5 {\int_0^{\pi /2} {\int_0^3 {r\cos \theta } dr} d\theta } dz \cr
& \int_{ - 1}^5 {\int_0^{\pi /2} {\left[ {\int_0^3 {r\cos \theta } dr} \right]} d\theta } dz \cr
& {\text{Integrate with respect to }}r \cr
& \int_0^3 {r\cos \theta } dr = \cos \theta \left[ {\frac{1}{2}{r^2}} \right]_0^3 \cr
& = \cos \theta \left[ {\frac{9}{2}} \right] \cr
& = \frac{9}{2}\cos \theta \cr
& \int_{ - 1}^5 {\int_0^{\pi /2} {\left[ {\int_0^3 {r\cos \theta } dr} \right]} d\theta } dz = \int_{ - 1}^5 {\int_0^{\pi /2} {\frac{9}{2}\cos \theta } d\theta } dz \cr
& {\text{Integrate with respect to }}\theta \cr
& \int_0^{\pi /2} {\frac{9}{2}\cos \theta } d\theta = \frac{9}{2}\left[ {\sin \theta } \right]_0^{\pi /2} \cr
& = \frac{9}{2}\left[ {\sin \left( {\frac{\pi }{2}} \right) - \sin \left( 0 \right)} \right] \cr
& = \frac{9}{2} \cr
& \int_{ - 1}^5 {\int_0^{\pi /2} {\frac{9}{2}\cos \theta } d\theta } dz = \int_{ - 1}^5 {\frac{9}{2}} dz \cr
& {\text{Integrate}} \cr
& = \frac{9}{2}\left[ z \right]_{ - 1}^5 \cr
& = \frac{9}{2}\left( {5 + 1} \right) \cr
& = 27 \cr} $$
