# Find curves C1 and C2 that are not closed

• March 18th 2008, 07:25 AM
enterprise-solutions
Find curves C1 and C2 that are not closed

Find curves C1 and C2 that are not closed and satisfy the equations

i) ∫C1 F•dr = 0

ii) ∫C2 F•dr = 1
• March 18th 2008, 07:41 AM
TheEmptySet
Quote:

Originally Posted by enterprise-solutions

Find curves C1 and C2 that are not closed and satisfy the equations

i) ∫C1 F•dr = 0

ii) ∫C2 F•dr = 1

1) for the first one since we want the integral equal to zero, The sine function equals zero when its argument is zero so set

$x+2y=0$ and we get..

$y=-\frac{x}{2}$

so any curve on that path will give an integral of zero.

for #2

using the fundemental theorem for line integrals

$\int_c= \overrightarrow{F} \cdot d \overrightarrow{r}=\nabla{f(r_2)}- \nabla{f(r_1)}$

so we need to pick a path that the difference of it's end point is 1.

so try

$(\frac{\pi}{2},0) \mbox{and} (0,0)$