Multivariable Calculus Quiz
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Let RR be a simply connected region in the plane and CC its positively oriented boundary. If F⃗=(P,Q)\vec{F} = (P, Q) is a vector field such that ∂P∂y=∂Q∂x\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x} throughout RR, and ∮CF⃗⋅dr⃗=15\oint_C \vec{F} \cdot d\vec{r} = 15, what can be concluded?
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