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

question 201

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $\mathbf { F } = x \mathrm { e } ^ { 3 \mathrm { x } ^ { 2 } } \mathbf { i } + \mathrm { e } ^ { 7 \mathrm { y } _ { j } } + \mathrm { e } ^ { 3 \mathrm { z } } \mathbf { k }$ ; the path is $\mathrm { C } _ { 1 } \cup \mathrm { C } _ { 2 }$ where $\mathrm { C } _ { 1 }$ is the straight line from $( 0,0,0 )$ to $( 1,1,0 )$ and $\mathrm { C } _ { 2 }$ is the straight line from $( 1,1,0 )$ to $( 1,1,1 )$

• A) \(W = \frac { e ^ { 3 } } { 6 } + \frac { e ^ { 7 } } { 7 } + \frac { e ^ { 3 } } { 3 }\)
• B) \(W = \frac { e ^ { 3 } - 1 } { 6 } + \frac { e ^ { 7 } - 1 } { 7 }\)
• C) \(W = \frac { e ^ { 3 } - 1 } { 6 } + \frac { e ^ { 7 } - 1 } { 7 } + \frac { e ^ { 3 } - 1 } { 3 }\)
• D) \(W = \frac { e ^ { 3 } - 1 } { 3 } + \frac { 2 e ^ { 7 } - 2 } { 7 } + \frac { e ^ { 3 } - 1 } { 3 }\)

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Definitions:

Work Tasks

Specific duties or assignments that are part of an individual's job role, contributing to the overall objectives of the workplace.

Raw Materials

are the basic, unprocessed materials used as inputs for manufacturing, construction, or other industrial processes.

Secondary Sector

The secondary sector encompasses industries involved in the manufacturing and processing of raw materials into finished goods and products.

Tertiary Sector

The segment of the economy that provides services rather than producing goods, including sectors like retail, education, and health care.