For each of the following, compute S a) S is the portion of the surface z x4 y2 which lies over the unit square 0, 1 0,1 , with upward pointing normal, and x dy dz y dz dx z dx dy b) S is the upper hemisphere z a2 x2 y2, with outward pointing normal, and x dy dz y dz dx c) S is the spherical cap z ...

a Using the trivial parameterization z x 4 y 2 we see that N 4x 3 2y 1 points upward Thus b B ...

For each of the following, compute S . a) S is the portion of the surface z

Question:

For each of the following, compute ∫∫S ω.
a) S is the portion of the surface z = x4 + y2 which lies over the unit square [0, 1] × [0,1], with upward-pointing normal, and ω = x dy dz + y dz dx + z dx dy.
b) S is the upper hemisphere z = √a2 - x2 - y2, with outward-pointing normal, and ω = x dy dz + y dz dx.
c) S is the spherical cap z = √a2 - x2 - y2 which lies inside the cylinder
x2 + y2 = b2, 0 < b < a, with upward-pointing normal, and w = xz dy dz + dz dx + zdx dy.
d) S is the truncated cone z = 2√x2 + y2, 0 < z < 2, with normal which points away from the z-axis, and ω = x dy dz + ydz dx + z2 dx dy.