Multivariable Calculus Quiz
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A vector field F⃗\vec{F} satisfies ∇×F⃗=0⃗\nabla \times \vec{F} = \vec{0} in a region RR, and ∫C1F⃗⋅dr⃗=8\int_{C_1} \vec{F} \cdot d\vec{r} = 8 where C1C_1 is a curve from point PP to point QQ lying entirely in RR. If C2C_2 is another curve from PP to QQ that passes through a small hole in region RR (where F⃗\vec{F} is undefined), which statement is necessarily true?
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