7. $\int_C y e^x dx + 2xe^y dy$,
C is the square with sides $x = 0$, $x = 1$, $y = 0$, and $y = 1$.
8. $\int_C x^2 y^2 dx + 4xy^3 dy$,
C is the triangle with vertices (0, 0), (1, 3), and (0, 3).
9. $\int_C (y + e^x) dx + (2x + \cos y^2) dy$,
C is the boundary of the region enclosed by the parabolas $y = x^2$ and $x = y^2$.
10. $\int_C xe^{-2x} dx + (x^4 + 2x^2 y^2) dy$,
C is the boundary of the region between the circles $x^2 + y^2 = 1$ and $x^2 + y^2 = 4$
