Evaluate the surface integral of G over the surface S.
-$\mathrm { S }$ is the portion of the cone $\mathrm { z } = 3 \sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } , 0 \leq \mathrm { z } \leq 3 ; \mathrm { G } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \mathrm { z } - \mathrm { y }$
A) $\frac { 2 } { 9 } \sqrt { 10 } \pi$
B) $\frac { 2 } { 3 } \sqrt { 10 } \pi$
C) $2 \sqrt { 10 }$
D) $2 \sqrt { 10 } \pi$

Question

Quizplus · Accepted Answer

The surface integral is evaluated by converting the cone into polar coordinates and integrating over the given limits. The symmetry and bounds of the cone lead to the result $2 \sqrt{10} \pi$.

Evaluate the Surface Integral of G Over the Surface S S\mathrm { S }S

Evaluate the Surface Integral of G Over the Surface S $\mathrm { S }$