Guse the divergence theorem to evaluat where f = d xz + x 2 , −2xy, x2 + z 2 e and s is the hemisphere z = p 4 − x 2 − y 2 together with the portion of the xy-plane beneath that hemisphere, oriented outward.

I guess you're supposed to evaluate the integral,

where and is the hemisphere .

has divergence

By the divergence theorem,

where is the space with as its boundary.

Convert to spherical coordinates, taking

Then the integral is

its the fourth option

you already gave the answer

step-by-step explanation: