Evaluate the surface integral where $S$ is the surface with parametric equations $x = 7 u v$, $y = 6 ( u + v ) , z = 6 ( u - v ) , u ^ { 2 } + v ^ { 2 } = 3$
$\iint _ { S } 10 y z d S$
Select the correct answer.
A) $I = 0$
B) $I = 10 + 7 \pi$
C) $I = 3$
D) $I = 10 \pi$
E) $I = 10 + 3 \pi$

Question

Quizplus · Accepted Answer

The surface integral evaluates to zero because the integrand $10yz$ is an odd function with respect to the symmetric limits of integration over the circular region $u^2 + v^2 = 3$.

Evaluate the Surface Integral Where SSS Is the Surface with Parametric Equations

Evaluate the Surface Integral Where $S$ Is the Surface with Parametric Equations