## Calculus 8th Edition

a) $C_1$ be any curve from $(0,0)$ to $(\pi,0)$ b) $C_2$ be any curve from $(0,0)$ to $(\dfrac{\pi}{2},0)$; (other answers are also possible)
a) Here, we have $\int_{C_1}F \cdot dr=\int_{C_1} \nabla F \cdot dr$ or, $\sin (r-2s)-\sin (p-2q)=0$ Thus, we get $C_1$ be any curve from $(0,0)$ to $(\pi,0)$ b) $\int_{C_1}F \cdot dr=\int_{C_1} \nabla F \cdot dr$ or, $\sin (r-2s)-\sin (p-2q)=1$ Thus, we get $C_2$ be any curve from $(0,0)$ to $(\dfrac{\pi}{2},0)$