Multivariable Calculus Quiz
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Let F(x,y)=(P(x,y),Q(x,y))\mathbf{F}(x,y) = (P(x,y), Q(x,y)) be a conservative vector field in a simply connected region DD, and let ff be a potential function for F\mathbf{F}. If ∫CF⋅dr=15\int_C \mathbf{F} \cdot d\mathbf{r} = 15 where CC is a curve from point A(1,2)A(1,2) to point B(3,4)B(3,4), what is ∫C′F⋅dr\int_{C'} \mathbf{F} \cdot d\mathbf{r} where C′C' is any curve from B(3,4)B(3,4) to A(1,2)A(1,2)?
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