Question: Let P(x, y, z) be the pressure at the point (x, y, z) in a fluid. Let F→ (x, y, z) = P(x, y, z)k→ . Let S be the surface of a body submerged in the fluid. If S is oriented inward, show that ∫SF→ · dA→ is the buoyant force on the body, that is, the force upward on the body due to the pressure of the fluid surrounding it.