Chapter 16.3, Problem 28E

Let $F=\nabla f$, where $f\left(x,y\right)=\sin \left(x-2y\right)$. Find curves $C_1$ and $C_2$ that are not closed and satisfy the equation.

(a) ${\displaystyle \underset{C_1}{\int }F\cdot dr=0}$

(b) ${\displaystyle \underset{C_2}{\int }F\cdot dr=0}$