Use Stokes' Theorem to evaluate $\oint _ { C } \mathbf { F } \cdot d \mathbf { r }$ . $\mathbf { F } ( x , y , z ) = 7 \cos x \mathbf { i } + 5 e ^ { y } \mathbf { j } + 2 x y \mathbf { k }$ ; C is the curve obtained by intersecting the cylinder $x ^ { 2 } + y ^ { 2 } = 1$ with the hyperbolic paraboloid $z = x ^ { 2 } - y ^ { 2 }$ , oriented in a counterclockwise direction when viewed from above
A) $- 2 \pi$
B) 0
C) $\pi$
D) $1$

Question

Quizplus · Accepted Answer

Stokes' Theorem can be applied because the vector field is conservative and the curve is closed.

Use Stokes' Theorem to Evaluate ∮CF⋅dr\oint _ { C } \mathbf { F } \cdot d \mathbf { r }∮C​F⋅dr

Use Stokes' Theorem to Evaluate $\oint _ { C } \mathbf { F } \cdot d \mathbf { r }$