State Stokes' Theorem $\int _ { C } \vec { F } \cdot \vec { d r } = \int _ { S } \operatorname { curl } \vec { F } \cdot \vec { d A }$

Multiple Choice

State Stokes' Theorem.

A) If S is a smooth oriented surface with smooth, oriented boundary C, then $\int _ { C } \vec { F } \cdot \vec { d r } = \int _ { S } \operatorname { curl } \vec { F } \cdot \vec { d A }$
B) If S is a smooth oriented surface with piecewise smooth, oriented boundary C, then $\int _ { S } \vec { F } \cdot \vec { d r } = \int _ { C } \operatorname { curl } \vec { F } \cdot \vec { d A }$
C) If S is a smooth oriented surface with piecewise smooth, oriented boundary C, then $\int _ { C } \vec { F } \cdot \vec { d r } = \int _ { S } \operatorname { cur } \vec { F } d V$
D) If S is a smooth oriented surface with piecewise smooth, oriented boundary C, and if $\vec { F }$ is a smooth vector field on an open region containing S and C, then
$\int _ { C } \vec { F } \cdot \vec{ d r } = \int _ { S } \operatorname { curl } \vec { F } \cdot \vec { d A }$
E) If S is a smooth oriented surface with piecewise smooth, oriented boundary C, then $\int _ { C } { \vec { F } } \cdot \vec { d r } = \int _ { S } d i v { \vec { F } } d V$