I'm studying for my exams coming up next week. The exercise is the following:
Let $\Omega \subset \mathbb R^2$ be a simply connected space of area equivalent to $2.$ Let $\gamma $ be a simple parametrization of $\delta \Omega$, where $\gamma (0) = (1,1)$ and $\gamma (1) = (1,0)$. Find:
$$\int_0^1 (ye^{xy}, xe^{xy}) \, d\gamma$$
$$\int_{\delta \Omega} (x,3y) \,dS$$
By Green's Theorem, the seond integral should be 0 (right?). However, I haveno idea what to do about the first one. Since we're not integrating on the whole boundary of Omega, I have no idea what to do. I also don't know what I should do with the given information on Omega's area
Furthermore, the integrand's curl is not zero, so I can't just draw a line between $(1,1)$ and $(1,0)$ and integrate over that.