Hello.

So basically I need to calculate this

where L is defined as

I decided to go for (Wikipedia link below, I assume notation is reasonably understandable)

but, no matter how shameful that is, I am not sure how to quickly define a projection (of the curve) to Oxy plane...

P.S. Moreover, since all this means some specific circulation, how differently should L be described if I wanted it to go the other way (and get the opposite value)?