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Counting Integrals.

Follow the white rabbit (algorithmic steps):

1. Decompose function into simple functions (simple functions counting is easier to optimize).
2. Count individual values of simple functions (integral values are numbers, values of the areas under curves).
3. Count result.

Riemann's Integral.

Riemann's Integral. photo riemann_zpsf8bd1453.png


Source: Wikipedia.

Complex function.

Complex function's value at point x can be constructed from simple function values at point x.

For example:

fs1(x) = x => fs1(3) = 3.
fs2(x) = 2 => fs1(3) = 2.
fc(x) = fs1(x) * fs2(x) => fc(3) = 3 * 2 = 6 <= fc(x) = 2 * x where: x = 3.


See also: Base-k arbitrary precision arithmetics implementation.

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