paulsoper / area-under-a-curve

Newton-Cotes formulae for finding the area under a curve

Numerical methods - at the moment all in c - for measuring the area under a curve.

Each method integrates the curve f(x) = 5x^3 - 12x^2 + 7x - 3, and the integration is carried out from x = 2 to x = 6.

The analytic answer is area = 868.00

The eight methods represented here are the eight Newton-Cotes formulae - four open and four closed.

The trapezoid rule is the first degree closed Newton-Cotes formula.

Simpson's rule is the second degree closed Newton-Cotes formula.

Simpson's 3/8 rule is the third degree closed Newton-Cotes formula.

Boole's rule is the fourth degree closed Newton-Cotes formula.

The rectangle rule is the second degree open Newton-Cotes formula.

The trapezoid method is the third degree open Newton-Cotes formula.

Milne's rule is the fourth degree open Newton-Cotes formula.

The fifth degree open Newton-Cotes formula has no name, and is in the program noname.c