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.
- $$\mathbf { F } = 3 \mathrm { y } \mathbf { i } + \sqrt { \mathrm { z } } \mathbf { j } + ( 4 \mathrm { x } + 3 \mathrm { z } ) \mathbf { k } ; \mathrm { C } : \mathbf { r } ( \mathrm { t } ) = \mathrm { t } \mathbf { i } + \mathrm { t } ^ { 2 } \mathbf { j } + \mathrm { t } , 0 \leq \mathrm { t } \leq 2$$

A) $W = 22 + 20 \sqrt { 2 }$
B) $W = 31 + 20 \sqrt { 2 }$
C) $W = 22 + \frac { 16 \sqrt { 2 } } { 5 }$
D) $W = 0$