numerical-integration

A set of numerical integration routines in C++.

The details

We will implement the following routines/algorithms for numerical integration:

Rectangle rule : this is as stupid as it gets
Trapezoidal rule : just a bit smarter than rectangle rule.
Iterated rule: break up the interval [a,b] into smaller pieces and use the rectangle or trapezoidal rule on these pieces, then add up these separate sums (this kind of looks like Riemann sums)
Simpson's rule: a numerical approximation to the definite integral credited to Thomas Simpson, a mathematician from the 1700s. It involves approximating the integrable function f by a polynomial P and then integrating that polynomial.
Adaptive quadrature: you integrate f over some interval, and you check the error with the real value of the integral. If it's too large, you integrate again, but over two different intervals, and with a smaller tolerance.