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 $2 \pi \int _ { a } ^ { b } g ( u ) \sqrt { \left[ g ^ { \prime } ( u ) \right] ^ { 2 } + \left[ f ^ { \prime } ( u ) \right] ^ { 2 } } \mathrm { du }$

Question

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 $2 \pi \int _ { a } ^ { b } g ( u ) \sqrt { \left[ g ^ { \prime } ( u ) \right] ^ { 2 } + \left[ f ^ { \prime } ( u ) \right] ^ { 2 } } \mathrm { du }$

Quizplus · Accepted Answer

The Answer of 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 $2 \pi \int _ { a } ^ { b } g ( u ) \sqrt { \left[ g ^ { \prime } ( u ) \right] ^ { 2 } + \left[ f ^ { \prime } ( u ) \right] ^ { 2 } } \mathrm { du }$

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

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