Find the Flux of the Curl of Field F Through

question 234

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = \mathrm { x } ^ { 2 } \mathrm { yi } - 3 x \mathrm { y } ^ { 2 } \mathbf { j } + \ln \mathrm { zk } ; \mathrm { S } : \mathrm { r } ( \mathrm { r } , \theta ) = \mathrm { r } \cos \theta \mathbf { i } + \mathrm { r } \sin \theta \mathbf { j } + 2 \mathrm { rk } , 0 \leq \mathrm { r } \leq 2$ and $0 \leq \theta \leq 2 \pi$

• A) \(- 16 \pi\)
• B) 16
• C) \(- 16\)
• D) \(24 \pi\)

---

Definitions:

Scientific Method

A systematic and empirical approach to research in which a problem is identified, relevant data are gathered, a hypothesis is formulated from these data, and the hypothesis is empirically tested.

Theory

A system of ideas intended to explain something, based on general principles independent of the thing to be explained.

Hypothesis

A testable prediction or explanation about a phenomenon that acts as a basis for further investigation.

Psychoanalytic Approach

A theory of psychology introduced by Sigmund Freud that emphasizes unconscious processes and childhood experiences as determinants of psychological development and issues.