State the Divergence Theorem.
A)If W is a solid region whose boundary S is a piecewise smooth surface, then $\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W } { div } { \vec { F} } d V$
B)If W is a solid region whose boundary S is a smooth surface oriented outward, then $\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W } { div } { \vec { F} } d V$
C)If W is a solid region whose boundary S is a piecewise smooth surface oriented outward, and if $\vec { F }$ is a smooth vector field on an open region containing W and S, then
$\int_{S} \vec{F} \cdot \overrightarrow{d A}=\int_{W} \operatorname{div} \vec{F} d V$
D)If W is a solid region whose boundary S is a piecewise smooth surface oriented outward, then $\int _ { S } \vec { F } \cdot \vec { d A } = \int _ { W } { div } \vec { F } \cdot \overrightarrow { d \bar { V } }$
E)If S is a solid region whose boundary W is a piecewise smooth surface oriented outward, then $\int _ { S } \vec { F } \cdot \vec { d A } = \int _ { W } { div } \vec { F } { d { V } }$

Question

State the Divergence Theorem.
A)If W is a solid region whose boundary S is a piecewise smooth surface, then $\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W }  { div }  { \vec { F} } d V$
B)If W is a solid region whose boundary S is a smooth surface oriented outward, then $\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W }  { div }  { \vec { F} } d V$
C)If W is a solid region whose boundary S is a piecewise smooth surface oriented outward, and if $\vec { F }$ is a smooth vector field on an open region containing W and S, then
$\int_{S} \vec{F} \cdot \overrightarrow{d A}=\int_{W} \operatorname{div} \vec{F} d V$
D)If W is a solid region whose boundary S is a piecewise smooth surface oriented outward, then $\int _ { S } \vec { F } \cdot \vec { d A } = \int _ { W }  { div } \vec { F } \cdot \overrightarrow { d \bar { V } }$
E)If S is a solid region whose boundary W is a piecewise smooth surface oriented outward, then $\int _ { S } \vec { F } \cdot \vec { d A } = \int _ { W }  { div } \vec { F }  { d  { V } }$

Quizplus · Accepted Answer

The Divergence Theorem states that if $W$ is a solid region bounded by a piecewise smooth surface $S$ oriented outward, and $\vec{F}$ is a smooth vector field defined on an open region containing $W$, then the flux of $\vec{F}$ across $S$ is equal to the integral of the divergence of $\vec{F}$ over the volume $W$. This is accurately represented in choice C.

State the Divergence Theorem ∫SH⃗⋅dA⃗=∫WdivF⃗dV\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W } { div } { \vec { F} } d V∫S​H⋅dA=∫W​divFdV

State the Divergence Theorem $\int _ { S } \vec { H } \cdot \vec { d A } = \int _ { W } { div } { \vec { F} } d V$