Calculate the Flow in the Field F Along the Path

Multiple Choice

Calculate the flow in the field F along the path C.
- $\mathbf { F } = - \frac { z y } { 6 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { i } + \frac { z x } { 6 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } j + \frac { z ^ { 3 } } { 3 \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \mathbf { k } , C$ is the curve $r ( t ) = 4 \cos 6 t i + 4 \sin 6 t j + 3 t k , 0 \leq t$ $\leq 1$

A) $\frac { 61 } { 9 }$
B) 21
C) $\frac { 61 } { 3 }$
D) 0