Chapter 16.4, Problem 5PQ

a.

To determine

To find:Value of the integral ${\displaystyle \underset{0}{\overset{\pi }{\int }}{\displaystyle \underset{0}{\overset{\pi }{\int }}{\displaystyle \underset{0}{\overset{3}{\int }}{\rho }^2\sin \varphi d\rho d\theta }}}$ .

b.

To determine

To find: Value of the integral ${\displaystyle \underset{0}{\overset{2\pi }{\int }}{\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}{\displaystyle \underset{0}{\overset{3}{\int }}{\rho }^2\sin \varphi drd\theta }}}$ .

c.

To determine

To find: Value of the integral ${\displaystyle \underset{0}{\overset{\pi /4}{\int }}{\displaystyle \underset{0}{\overset{\pi /2}{\int }}{\displaystyle \underset{0}{\overset{3}{\int }}{\rho }^2\sin \varphi d\rho d\theta }}}$ .

d.

To determine

To find: Value of the integral ${\displaystyle \underset{-\pi /4}{\overset{\pi /4}{\int }}{\displaystyle \underset{0}{\overset{\pi }{\int }}{\displaystyle \underset{0}{\overset{3}{\int }}{\rho }^2\sin \varphi d\rho d\theta }}}$ .