Evaluate the surface integral. s x2 + y2 + z2 ds s is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 and z = 3, together with its top and bottom disks

Parameterize the lateral face of the cylinder by



where and , and parameterize the disks as




where and .

The integral along the surface of the cylinder (with outward/positive orientation) is then

Sis less than or equal to 75 (bottom left)