Using the Divergence Theorem, Find the Outward Flux of F

question 121

Multiple Choice

Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.
- $$\mathbf { F } = x ^ { 2 } \mathbf { i } + y ^ { 2 } \mathbf { j } + z \mathbf { k } \text {; D: the solid cube cut by the coordinate planes and the planes } x = 3 , y = 3 \text {, and } z = 3$$

• A) 189
• B) 164
• C) 81
• D) 108

---

Definitions:

Aircraft

A vehicle designed to navigate through the air.

Returns to Scale

The change in output resulting from a proportional change in all inputs (factors of production) in the long run.

Inputs

Resources such as labor, materials, and capital that are used in the production process to create goods or services.

Output

The total amount of goods or services produced by a firm, industry, or economy over a certain period of time.