Chapter 16 - Vector Calculus - 16.3 The Fundamental Theorem for Line Integrals - 16.3 Exercises - Page 1135: 28

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 $(\dfrac{\pi}{2},0)$