Abstract In this work, three different integration techniques, which are the numerical, semi-analytical and exact integration techniques are briefly reviewed. Numerical integrations are carried out using three different Quadrature rules, which are the Classical Gauss Quadrature, Gauss Legendre and Generalized Gaussian Quadrature. Line integral method is used to perform semi-analytical integrati...

Quadrature rules estimate ∫ 1 0 f(x) dx when f is defined by a table of n+1 values. Every binary string of length n defines a quadrature rule by choosing which endpoint of each interval represents the interval. The standard rules, such as Simpson’s Rule, correspond to strings of low Kolmogorov complexity, making it possible to define new quadrature rules with no smoothness assumptions, as well ...