Newton-Cotes Quadrature

implementation rules

• Midpoint rule $M(f)=(b-a)f(\frac{a+b}{2})$
• Trapezoidal rule $T(f)=\frac{b-a}{2}f(f(a)+f(b))$
• Simpson’s rule $S(f)=\frac{b-a}{6}(f(a)+5f(m)+f(b))$

exact for $n$ node

up to $n$ degree