Define $f(x,y)=\int_c (2\xi\eta)d\xi + (\xi^2 −\eta^2)d\eta$ where $c$ is the straight line path from $(0,0)$ to $(x,y)$.
Compute $f(x,y)$ and its differential $df$ (in terms of $(x,y)$).
Normally, I know how to compute $f(x,y)$ and its differential if the provided one-form is in terms of $x$ and $y$, but in this problem the one-form uses $\xi$ and $\eta$, even though the function $f$ uses $x$ and $y$? I'm not sure I understand how this works and how it will change the procedure of solving the integral.