Thread: Line Integrals

For F = (4xy - 3(x^2)(z^2))i + (2(x^2))j - (2(x^3)z)k

(1,0,1) to (1,1,1)

Show the integral (lower limit c) F.dr is independent of the curve c joining two given points by obtaining a scalar function phi such that F = delta phi. Find the value of the integral between the points given.

I can find phi

2(x^2)y - (x^3)(z^2) + c

But i cant do the integral, what am i integrating? phi?

Just find

That integral is independent of the path because there exist a function
phi(x,y,z) such that
d phi= (4xy - 3(x^2)(z^2))dx + (2(x^2))dy - (2(x^3)z)dz