Path independence? 13-19 from check, and if independent, integrate from (0, 0, 0) to (a, b, c) 13. 2e (x cos 2y dx - sin 2y dy)

The integral is path-independent if there is a scalar function whose gradient is

(at least, that's what it looks like the given integrand is)

Then

Differentiating both sides with respect to gives

so the line integral *is* dependent on the path. (again, assuming what I've written above actually reflects what the question is asking)

a: 1/6, j: 1/4

step-by-step explanation: you are welcome