Find an expression for the surface area - where s is the

Question

Question 1: Find an expression for the surface area if z = f (x, y).

Question 2: Evaluate ∫_s∫z² dS where S is the unit sphere centred at the origin.

Question 3: Let S be the closed cylinder x² + y² = 9, z = 0, z= 15. Find ∫_s∫z dS

Question 4: Find ∫_s∫x dS where S is the triangle with vertices (1,0,0), (0,1,0) and (0,0,1).

Question 5: Evaluate ∫_s∫ F.dS where F(x,y,z) = (x,y,z) and S is the unit sphere centred at (0,0,0).

Question 6: Evaluate

∫_s∫(x³i + y³j).dS

where S is the closed cylinder

x² + y² = 4, z = 0 z = 5.