## Calculus: Early Transcendentals 8th Edition

a) Along x=-3, the vectors of F have positive y-components so since the path goes upward, $F\cdot T$ is always positive. Therefore $\int_{C_{1}}F\cdot dr$ = $\int_{C_{1}}F\cdot T ds$ is positive. b) All nonzero field vectors along the circle with radius 3 are pointed in the clockwise direction, opposite the direction to the path. Therefore $F\cdot T$ is negative and $\int_{C_{2}}F\cdot dr$ = $\int_{C_{2}}F\cdot T ds$ is negative.