Hello (sorry for bad usage of English)
i have some issue with this (got to much rusty on this). I need to proof that:
(I try to do it like this... so if I'm wrong or there's "smarter" way to do it i would be very grateful... perhaps i go way back to show what integral is... don't now... please help )
Let the complex function is defined in region and let the be smooth oriented curve with starting point A and end point B. We make division like so:
and make than even finer division:
where (k = 1,2,3,...,n)
where point is point between points and
we form integral sum for division
so we pot this all back in integral sum... and have:
than we have definition...
"For complex number I we say it's Riemman's integral of the complex function f(z) on curve l from point A to point B if and only if :
if I exists than we can write...
so if this exists than if we have some complex function g(z) = c f(z) where c is constant than we can say that :
and since c is constant than c can come in front of sum and limit so ....
and we can say that we can write
I think this is way to simple to write this much (if it's true)... but I don't know and that's why i need help...
and one more thing... how to proof that :
where A is constant, but without using Newton-Leibniz formula ?!
(it all seems to be trivial until i got start... or I'm just complicating it for myself )
Thanks for any help
thanks question goes like ::
if f(z) is integrable function, show that
there's nothing more to the question (and yes this one is about indefinite integrals.... second proof is for finite integrals )