The fundmental thereom of line integrals

[nameVoid]

show that the line integral is indpendant of path and evaluate the integral on interval (0,1),(1,2)
int c 1-ye^{-x}dx+e^{-x}dy

can someone show me the procedure here looks like they just integrated 1-ye^(-x) on x to get 2/e I get a diffrent answer if I integrate e^(-x) on y same interval do I just find a potential function f with F = 1-ye^-x,e^-x

 

[tiny-tim]

hi nameVoid!

(have an integral: ∫ and try using the X² icon just above the Reply box )

show that the line integral is indpendant of path
…
do I just find a potential function f with F = 1-ye^-x,e^-x

yes, you can either do that (there's a fairly obvious f ),

or you can show that the curl is zero

and evaluate the integral on interval (0,1),(1,2)
int c 1-ye^{-x}dx+e^{-x}dy

can someone show me the procedure here looks like they just integrated 1-ye^(-x) on x to get 2/e I get a diffrent answer if I integrate e^(-x) on y same interval

if you get different answers, you've probably used the wrong limits …

show us your full calculations, and then we'll see what went wrong!