f = gradƒ, where ƒ(x,y)=sin(x-2y)

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

i) ∫C1 F•dr = 0

ii) ∫C2 F•dr = 1

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- Mar 18th 2008, 08:25 AMenterprise-solutionsFind curves C1 and C2 that are not closed
f = gradƒ, where ƒ(x,y)=sin(x-2y)

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

i) ∫C1 F•dr = 0

ii) ∫C2 F•dr = 1 - Mar 18th 2008, 08:41 AMTheEmptySet

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

and we get..

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

for #2

using the fundemental theorem for line integrals

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

so try