(915, #23) Is the vector field below conservative? Explain.

Solution: If a vector field is conservative, then, on any closed path C,

.

If we take C to be some circle centered at the origin, oriented counterclockwise,

then the angles created by the vectors of F and the tangents to the circular path will be greater than ninety degrees. The cosine value of a number greater than ninety degrees is negative. Therefore the integrand is negative, making it not conservative.

by C.A.H.