Let $\mathbf { F } = \nabla f ,$ Where $f ( x , y ) = \sin ( x - 8 y )$

Multiple Choice

Let $\mathbf { F } = \nabla f ,$ where $f ( x , y ) = \sin ( x - 8 y )$ . Which of the following equations does the line segment from $( 0,0 )$ to $( 0 , \pi )$ satisy?

A) $\int _ { C } \mathbf { F } \cdot d \mathbf { r } = 0$
B) $\int _ { C } \mathbf { F } \cdot d \mathbf { r } = 1$
C) none of these