Let the surface S be part of the sphere r +y² +z² = 4 (oriented away from the origin) that lies within the cylinder r² + y² = 1 and above the plane z = 0, and let n denote the unit normal vector in the direction of the orientation. Let C be the boundary curve of S. Consider the vector ficld F(x, y, z) = ri + yj+ xyzk. %3D (a) Evaluate the line integral F.T dS directly, without using Stokes' Theorem, where T is a unit tangent vector to the curve C. (b) Evaluate the surface integral | S (V × F) - n dS directly, without using Stokes' Theorem.

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