For my homework I have to take the path integral of $F=<\arccos x,xy-e^y>$ over the triangular path from $(0,0)$ to $(2,3)$ to $(2,0)$ and back to $(0,0)$. I have broken this integral into three separate integrals, and my first integral looks like this:
$$ \int <\arccos(2t), 6t^2-e^{3t}>• <2,3>dt$$
However this is leading to some crazy results with imaginary numbers... am i setting this up wrong?
Hint: What is the value of the integral of $g(x) dx$ over a closed path in $\mathbb{R}^2$ ?