Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2y3zi + sin xyzj + xyzk, S is the part of the cone y2 = x2 + z2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.

Why do we use the line integral form of stokes theorem to integrate this, instead of the stokes variation that uses the curl?