How to find the midpoint of the area of ​​a complex figure?

Question

C++ / C#

Hello! A problem arose - you need to find the middle of the area of ​​​​complex figures, that is, the line along 0x, which will divide this figure in half.
I tried to do it through the squares, but I always got an inaccurate answer.

Answer 1

To solve the problem, you must be able to find:
Stotal - the area of ​​the entire figure.
SL(x) - the area of ​​the figure located to the left of the line x
The function SL(x) is non-decreasing, continuous, to the left of the figure it is equal to 0, to the right of the figure it is equal to Stot.
It follows from this that there is such a value xс, at which SL(xс) = 0.5 Stotal.
Analytically, it can be found only for certain cases.
It can be found by numerical methods - in several stages: we take x1, calculate SL(x1), if Stotal is greater than 0.5, we shift to the left, if less - to the right, and so on, until we get closer to the accuracy we need.