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

Multiple Choice

Find the work done by F over the curve in the direction of increasing t.
- $\mathbf { F } = 6 x \mathbf { i } - 6 \mathrm { x } ^ { 5 } \mathrm { y } ^ { 4 } \mathbf { j } + \left( - 3 \mathrm { z } - 7 \mathrm { y } ^ { 2 } \right) \mathbf { k }$ ; the path is $\mathrm { C } _ { 1 } \cup \mathrm { C } _ { 2 } \cup \mathrm { C } _ { 3 }$ where $\mathrm { C } _ { 1 }$ is the straight line from $( 0,0,0 )$ to $( 1,0,0 ) , \mathrm { C } _ { 2 }$ is the straight line from $( 1,0,0 )$ to $( 1,1,0 )$ , and $C _ { 3 }$ is the straight line from $( 1,1,0 )$ to $( 1,1,1 )$

A) $W = - \frac { 67 } { 10 }$
B) $W = \frac { 9 } { 5 }$
C) $W = - \frac { 57 } { 10 }$
D) $W = 3$