Use the Divergence Theorem to Calculate the Surface Integral $\iint _ { s } \mathbf { F } \cdot d \mathbf { S }$

question 86

Short Answer

Use the Divergence Theorem to calculate the surface integral $\iint _ { s } \mathbf { F } \cdot d \mathbf { S }$ ; that is, calculate the flux of $\mathbf { F }$ across $S$ .
$$\mathbf { F } ( x , y , z ) = x y e ^ { z } \mathbf { i } + x y ^ { 2 } z ^ { 3 } \mathbf { j } - y e ^ { z } \mathbf { k }$$
$S$ is the surface of the box bounded by the coordinate planes and the planes $x = 6 , y = 2$ and $z = 1$ .

---

Definitions:

Maladaptive Explanations

Reasoning or explanations that are not beneficial and may hinder an individual's ability to adapt or cope with situations.

Self-defeating Beliefs

Negative beliefs about oneself that hinder personal development or success.

Unresolved Anger

Persistent feelings of anger or resentment that have not been addressed or expressed, potentially leading to negative emotional and physical outcomes.

Psychoanalytic Perspective

A psychological approach that emphasizes the influence of the unconscious mind on behavior, developed by Freud.