Find the Work Done by F Over the Curve in the Direction

question 215

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $$\mathbf { F } = - \frac { 1 } { 16 \mathrm { x } ^ { 2 } } \mathbf { i } + \frac { 3 \mathrm { z } } { 4 \mathrm { x } } \mathbf { j } + \frac { 1 } { 48 \mathrm { x } ^ { 2 } } \mathbf { k } ; \mathrm { C } : \mathbf { r } ( \mathrm { t } ) = \frac { \cos 4 \mathrm { t } } { 4 } \mathbf { i } + \frac { \sin 4 \mathrm { t } } { 4 } \mathbf { j } + 3 \mathrm { t } \mathbf { k } , 0 \leq \mathrm { t } \leq \frac { \pi } { 16 }$$

• A) \(W = \frac { \sqrt { 2 } } { 4 } + \frac { 9 } { 256 } \pi ^ { 2 }\)
• B) \(W = \frac { \sqrt { 2 } } { 4 } + \frac { 9 } { 512 } \pi ^ { 2 }\)
• C) \(W = \frac { \sqrt { 2 } } { 8 } + \frac { 9 } { 512 } \pi ^ { 2 }\)
• D) \(W = \frac { \sqrt { 2 } + 2 } { 4 } + \frac { 9 } { 512 } \pi ^ { 2 }\)

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Definitions:

Four Tests

A set of criteria or checks used to evaluate the validity or reliability of a concept, argument, or piece of evidence.

Comparative Inferences

The process of deducing conclusions by examining the similarities or differences between two or more objects, scenarios, or datasets.

Comprehensiveness

Refers to the quality of including all or nearly all elements or aspects of something.

Comparative Reasoning

Evaluating two or more objects, ideas, or situations to identify similarities and differences.