How would you solve the following difficult problem below?

Question

For the force field F(x,y,z)=(ze^x cos y) i - (ze^x sin y) j + (e^x cos y) k, calculate the work done by F on an object moving along a curve from (0, 0, 0) to (2, π/2, 1)


these were the possible answers given....

-2
-2 - 4e^2
0
-2e
-3e^2
-4e^2

Answer 1

First we must see if it is a potential field
Px= z e^x cosy so P = z e^x cosy +f(y,z)
Py =- z e^xsin y so P = z e^x cos y +h(xz)
Pz = e^x cos y so P= z e^x cos y + g(x,y)
so
P= z e^x cos y is the potential function and the integral is

1*e^2*0- 0*1*1=0