# Let \vec{F}(x, y, z) = -4z \vec{i} + 3x \vec{k} and S be the closed square pyramid with height 14...

## Question:

Let {eq}\vec{F}(x, y, z) = -4z \vec{i} + 3x \vec{k} {/eq} and {eq}S {/eq} be the closed square pyramid with height {eq}14 {/eq} and base on the {eq}xy {/eq}-plane with side length {eq}3 {/eq}. The pyramid {eq}S {/eq} is oriented outward. Compute the flux of {eq}\vec{F} {/eq} through {eq}S {/eq}.

## Computing the Flux:

For computing the flux, we have to use the Gauss Divergence theorem.

The general form of the Gauss Divergence theorem is {eq}\iint_{S} \vec{F} \cdot d\vec{A} = \iiint_{V} div F \ dV {/eq}

By applying the given function in the general form.

Then evaluate the function to get a resultant part.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answerThe given vector field is {eq}\vec{F}\left ( x, y, z \right ) = -4z \vec{i} + 3x \vec{k} {/eq}.

Where {eq}S {/eq} be the closed square pyramid.

An...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 16 / Lesson 2The fundamental theorem of calculus makes finding your definite integral almost a piece of cake. See how the definite integral becomes a subtraction problem after applying the fundamental theorem of calculus.