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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