Let be a differentiable 1-1 mapping of onto such that and and .
Then by the chain rule.
Now substitute , giving .
Let be a continuous function over a curve parametrized by .
If is a reparametrization of that inverts the orientation, show that .
My attempt : I still didn't find the main idea of the proof. Stuck at starting. I think I've seen a similar proof in calculus 3, but I don't remember it.