Copyright C Cengage Learning All Rights Reserved Partial Derivatives Ppt Download
θ d θ d ϕ which is really hard to evaluate But we know that the normal vector to the sphere is r = ( x, y, z), hence, (2) ∬ S F r d S = ∬ S ( x 2, y 2, z 2) ⋅ ( x, y, z) d S = ∬ S ( x 3 y 3 z 3) d S = ∬ S ( x 3 y 3) d S ∬ S z 3 d S Can we say that the first summand evaluates to zero since S is symmetrical with respect to the x and yaxes?Calculate surface integral ∬ S f (x, y, z) d S, ∬ S f (x, y, z) d S, where f (x, y, z) = z 2 f (x, y, z) = z 2 and S is the surface that consists of the piece of sphere x 2 y 2 z 2 = 4 x 2 y 2 z 2 = 4 that lies on or above plane z = 1 z = 1 and the disk that is enclosed by intersection plane z = 1 z = 1 and the given sphere (Figure 672)
