
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?


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