Use Stokes' Theorem to Evaluate $\iint _ { S } \operatorname { cur } \mathbf { F } \cdot d \mathbf { S }$

question 7

Short Answer

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { cur } \mathbf { F } \cdot d \mathbf { S }$ .
$$\mathbf { F } ( x , y , z ) = 9 x y \mathbf { i } + 6 y z \mathbf { j } + 9 z ^ { 2 } \mathbf { k }$$ $S$ is the part of the ellipsoid $4 x ^ { 2 } + 4 y ^ { 2 } + 49 z ^ { 2 } = 196$ lying above the $x y$ -plane and oriented with normal pointing upward.

---

Definitions:

Psychological Factors

Refers to the mental, emotional, and cognitive aspects that influence an individual's behavior and well-being.

Abnormal Functioning

A term referring to patterns of behavior, thought, or emotions considered outside the societal norm, possibly indicating a psychological disorder.

Somatogenic Approach

A theoretical approach in psychology and psychiatry that emphasizes the physical causes of mental disorders, focusing on genetic, neurological, or biochemical contributors.

Psychogenic Approach

Psychological factors as the primary cause behind physical symptoms or diseases.