Question

Show that the line integral is independent of path, and evaluate the integral.

∫(c) y dx + (x+z) dy + y dz; C is parametrized by

r(t)= (t^2+1)/(t^2-1) i +cos(pi)t j + 2tsin(pi)t k

for 0<_ t <_ 1/2

Answer 1

it is not related to C so just initial and final point
(-1 , 1 , 0) to ((-5/3 , 0 , 2)
int=xy+yz

Answer 2

So thE answer is going to be 0-(-1)=1