Evaluate integral_C vector F middot d vector r where vector F(x, y, z) = z vector i + xy vector j - y^2 vector k along the curve C given by vector r(t) = t^2 vector i + t vector j + squareroot t vector k. 0 lessthanorequalto t lessthanorequalto 1. Find the work done by the conservative field vector F(x, y, z) = yz vector i + xz vector j - xy vector k = vector nabla f, where f(x, y, z) = xyz along any smooth curve C joining the point A(-1,2,5) to B (1,6,-3). Show that vector F (x, y, z) = (y sin z) vector i + ( sin z) vector j + 9xy cos z) vector k Conservative or not?
