Answer
$$\dfrac{2}{5}$$
Work Step by Step
Our aim is to integrate the integral as follows:
$$\int^{\pi/2}_{-\pi/2} \int^1_0 \int^{r \cos \theta}_0 \space r^3 \space dz \space dr \space d\theta =\int^{\pi/2}_{-\pi/2} \int^1_0 r^4 \times \cos\theta \space dr \space d\theta \\=(\dfrac{1}{5}) \times \int^{\pi/2}_{-\pi/2} \cos\theta \\=\dfrac{2}{5}$$
