Use the Divergence Theorem to Evaluate Where F(x, Y $\sigma$

question 35

Essay

Use the divergence theorem to evaluate where F(x, y, z) = (x³ + 3xy²)i + z³ k, n is the outer unit normal to $\sigma$ , and $\sigma$ is the surface of the sphere of radius a centered at the origin.

---

Definitions:

Insomnia

A sleep disorder where individuals have difficulty falling asleep, staying asleep, or experience non-restorative sleep, leading to distress or impairment in daily functioning.

Mental Flexibility

The ability to adapt one's thinking and behavior in response to changing circumstances or new information.

Creativity

The ability to produce original and valuable ideas or solutions by thinking outside the conventional boundaries.

Sigmund Freud

An Austrian neurologist and the founder of psychoanalysis, a clinical method for treating psychopathology through dialogue between a patient and a psychoanalyst.