$\text { Use Stokes's Theorem to evaluate } \int _ { C } \overrightarrow { \mathbf { F } } \cdot d \overrightarrow { \mathbf { r } }$

question 14

Multiple Choice

$\text { Use Stokes's Theorem to evaluate } \int _ { C } \overrightarrow { \mathbf { F } } \cdot d \overrightarrow { \mathbf { r } }$ Use a computer algebra system to verify your results.
Note: $C$ is oriented counterclockwise as viewed from above.
$\begin{array} { l } \overrightarrow { \mathbf { F } } ( x , y , z ) = x y z \hat { \mathbf { i } } + y \hat { \mathbf { j } } + z \hat { \mathbf { k } } \\S : z = x ^ { 2 } , 0 \leq x \leq 3,0 \leq y \leq 3\end{array}$

• A) \(- \frac { 243 } { 4 }\)
• B) \(\frac { 243 } { 4 }\)
• C) \(- \frac { 27 } { 4 }\)
• D) \(\frac { 9 } { 4 }\)
• E) \(\frac { 27 } { 4 }\)

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Definitions:

Mnemonic Devices

Techniques a person can use to help them improve their ability to remember something.

Retroactive Interference

The phenomenon where newly acquired information hinders the recall of previously learned information.

Anterograde Amnesia

A condition characterized by an inability to form new memories following the onset of the disorder, though long-term memories from before the event remain intact.

Encoding Failure

A situation where the brain fails to create a memory link to information, making it difficult to remember later.