Integral, Curve length (Arc length)
This page is revision of Riemann integral using curve length problem.
That is the sum of the values of length a.
It will be done by making every interval very small, but as for a Riemann integral, it must be the sum of rectangles under curve. What curve?
The point c of the mean value theorem of Lagrange is used for it.
ui is the point c of the mean value theorem of Lagrande in every interval.
The height of rectangle is expressed with g(x).
The limit of the Riemann sum of g(x) will be the answer.
Riemann sum is a kind of rectangle method. Riemann integral is the limit of the sum of rectangles.
There were four curves for the solution.
The initial curves of the problem.
f(x)
g(x)
G(x)