(915, #9) Determine whether or not F(x,y) = < y e^x +sin(y), e^x + x cos(y) > is a conservative vector field. If it is, find a potential.

Solution: Write F = < f_x , f_y >for some f. Then:

Therefore the vector field is conservative.

Finding f:

We integrate f_x with respect to x.

We then differentiate f with respect to y.

We compare this to the given f_y and solve for g(y).

by C.A.H.