I am doing the problem
Calculate the work done in a moving particle along the given path
$F=<yze^x+xyze^x,xze^x,xye^x>$ along $C: r(t)= <2\cos t,3\sin t,0>$
$1≤t≤2$
I found that this field was conservative, so I was able to set up a potential function
$f=xyze^x+C$
From there to calculate work I did
$f_{end}-f_{start} $
This gives me zero though because of the z component. Is this correct or am I doing something wrong? Thanks in advance.
Edit: Showing requested work
$r(t)= <2\cos t,3\sin t,0>$ $1≤t≤2$
$r(1)= <2\cos(1),3\sin (1),0>$
$r(2)= <2\cos (2),3\sin (2),0>$
$f_{end}-f_{start} $
$ 0 - 0 = 0 $