University Calculus: Early Transcendentals (3rd Edition)

$$\dfrac{28\pi}{3\sqrt{3}}$$
Our aim is to integrate the integral as follows: $$\int^{\pi/3}_{\pi/6} \int^{2 \csc\phi}_{\csc\phi} \int^{2\pi}_0 p^2\sin \phi \space d\theta \space dp \space d\phi =2\pi \int^{\pi/3}_{\pi/6} \int^{2 \csc\phi}_{\csc\phi} p^2 \space\sin\phi dp \space d\phi \\=\dfrac{2\pi}{3}\int^{\pi/3}_{\pi/6} [ p^3 \times \sin\phi]^{2 \csc\phi}_{\csc\phi} \space dp \\=\dfrac{14\pi}{3} \times \int^{\pi/3}_{\pi/6} \csc^2\phi \space d\phi \\=\dfrac{28\pi}{3\sqrt{3}}$$