Solve the Problem $C : ( f ( u ) , g ( u ) )$

Essay

Solve the problem.
-Suppose that the parametrized plane curve $C : ( f ( u ) , g ( u ) )$ is revolved about the $x$ -axis, where $g ( u ) > 0$ and a $\leq u \leq$ b. Show that the surface area of the surface of revolution is $2 \pi \int _ { a } ^ { b } g ( u ) \sqrt { \left[ g ^ { \prime } ( u ) \right] ^ { 2 } + \left[ f ^ { \prime } ( u ) \right] ^ { 2 } } \mathrm { du }$