Line Integrals: Let F be a conservative vector field over...

[Daniel_Feldman]

Let F be a conservative vector field equal to the gradient of f, where f(x,y)=sin(y-2x). I need to find two curves C1 and C2 (that aren't closed) which satisfy the equations

=0

for curve C1, and

=1

for curve C2

 

[pka]

Re: Line Integrals

Let F be a conservative vector field equal to the gradient of f, where f(x,y)=sin(y-2x). I need to find two curves C1 and C2 (that aren't closed) which satisfy the equations

=0 for curve C1, and

=1 for curve C2

I wonder if that question is using standard definitions, if it is then it trivial.
The integrals of conservative fields are path independent.

Use two line segments: \(\displaystyle \begin{array}{l}
C_1 0,0) \to \left( {\frac{\pi }{2},\pi } \right) \\
C_2 :\left( {0,0} \right) \to \left( {0,\frac{\pi }{2}} \right) \\
\end{array}.\)