Chapter 15.2, Problem 14ES

In each part, evaluate the integral ${\displaystyle {\int }_C^{}ydx}+zdy-xdz$ along the stated curve

(a) The line segment from (0, 0, 0) to (1, 1, 1).

(b) The twisted cubic $x=t,y=t^2,z=t^3$ from (0, 0, 0) to (1, 1, 1).

(c) the helix $x=\cos \pi t,y=\sin \pi t,z=t\text{from (1,}\text{0,}\text{0) to (}-1,0,1).$