What is the algorithm for calculating the length of a bezier curve?

Question

Mathematics

Greetings!
It is necessary to calculate the length of the Bezier curve, I
did it head-on using Wikipedia ,
i.e. dividing the curve into straight segments with a step of 0.01
and this is where the essence of the problem lies - there are too large errors on long curves.
if I set the step to 0.0001, the error suits,
but then the process is too long for one straight line, and when there are 100 of them, you can have time to smoke.
At first I tried to split with a step of 0.1, look at the length, if it is long, then split it with a step of 0.0001, but only slightly increased performance
Interested in whether there are any algorithms for calculating the length without splitting into segments?
or maybe kick in the right direction =)

Answer 1

https://www.google.ru/search?q=%D0%B2%D1%8B%D1%87%...
well, that is, you take a parametric bezier function and integrate it analytically
and you get the formula for the length of your curve