- #1

Contingency

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## Homework Statement

[itex]\vec { F } \left( x,y \right) =u\left( x,y \right) \hat { i } +v\left( x,y \right) \hat { j }[/itex]

[itex]u\left( x,y \right) , v\left( x,y \right)[/itex] are continuous on ℝ²

[itex]\Gamma[/itex] is piecewise smooth.

Is [itex]\psi (x,y){ =\int { \vec { F } \left( x,y \right) \cdot \vec { dr } } }[/itex] differentiable? How can I show this if it is?

ψ is meant to be the line integral over Γ.

## Homework Equations

Definition of differentiability; definition of partial derivatives; formula for calculating line integrals under a parametrization.

## The Attempt at a Solution

I wanted to show that the partial derivatives of ψ are continuous, which would imply differentiability. I can't deal with ψ as it's defined, only with the formula, and I think differentiability must be independent of some arbitrary parametrization..

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