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

Question

Quizplus · Accepted Answer

The surface integral evaluates to zero because the surface is symmetric with respect to the yz-plane, and the integrand $10yz$ is an odd function in terms of $u$ and $v$.

Evaluate the Surface Integral Where S Is the Surface with Parametric