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


I’ve gotten this far with it….
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

Now how would you go about solving this….?

Answer 1

F=

For the function f(x,y,z)=ze^x(cosy), the gradient of f is equal to the field F.

So, by definition, F is conservative. We can thus use the Fundamental theorem for line integrals to get:

f(2, pi/2, 1)- f(0,0,0)=0

Answer 2

You are using my answer which is correct as you have only two points and the work depends on the initial end final point ONLY if it is done by a vector which comes from a potential function

Answer 3

Well the internagal function had been declined of a positive integer! here is how the problem should read:

bacon/pie = -cake/pie + reciprical of cake/bacon ^basin % princpal of the symetrical fruit cup!

DUH!