The answer is -3π4 or 3π4 ? Help me check the answer. thank you

Question

Show that the force field F(x,y,z)=(y²z³cosx-4x³z)i+(2z³ysinx)j+(3y²z²sinx-x⁴)k is conservative and find its potential function. Hence find the work done by F(x,y,z) in moving an object from (π,1,3) to (3,4,1) and then to (0,2,0).

Answer 1

Since F is the gradient of scalar field g(x,y,z) = y²z³sin x - x⁴z (so in particular F is conservative with a potential g) the work done by F along the path described is g(0,2,0) - g(π,1,3) = 0 - 3π⁴ = -3π⁴.