(b) Let $F(x, y) = (2xe^{x^2+y^2}, 2ye^{x^2+y^2})$ be a vector field.
i. Argue that F is conservative without looking for a potential. [6 marks]
ii. Find a potential for F.
[8 marks]
iii. Thus, or otherwise, determine $\int_C F \cdot dl$, where C is the oriented graph of sin(x) with x running from 0 to 2$\pi$. Clearly state the name of any theorem you use.
[4 marks]