Let $\mathbf { F } ( x , y , z ) = x ^ { 2 } y \mathbf { i } + y ^ { 2 } \mathbf { j } + x z \mathbf { k }$ and S is in the first octant bounded by and the coordinate planes. Using the Divergence Theorem, $\iint S$ $x = 1 ,$ is

A)2
B)3
C)4
D)5
E)6

Question

Let

\mathbf { F } ( x , y , z ) = x ^ { 2 } y \mathbf { i } + y ^ { 2 } \mathbf { j } + x z \mathbf { k }

and S is in the first octant bounded by and the coordinate planes. Using the Divergence Theorem,

\iint S

x = 1 ,

is

A)2
B)3
C)4
D)5
E)6

Quizplus · Accepted Answer

The divergence of $\mathbf{F}$ is $\nabla \cdot \mathbf{F} = 2xy + 2y + x$. Integrating over the region $0 \leq y \leq 1$, $0 \leq z \leq 1$, and $0 \leq x \leq 1$, the result is 2.

Let F(x,y,z)=x2yi+y2j+xzk\mathbf { F } ( x , y , z ) = x ^ { 2 } y \mathbf { i } + y ^ { 2 } \mathbf { j } + x z \mathbf { k }F(x,y,z)=x2yi+y2j+xzk

Let $\mathbf { F } ( x , y , z ) = x ^ { 2 } y \mathbf { i } + y ^ { 2 } \mathbf { j } + x z \mathbf { k }$