Relative Accuracy of Numerical Quadrature Formulas - Trapezoid Rule, Simpson's 1/3 Rule, Simpson's 3/8 Rule and Boole's Rule

We have calculated the definite integral by dividing the interval of integration [-1, 1] into 96 equal parts in trapezoidal rule, 192 equal parts in Simpson’s 1/3 rule, 288 equal parts in Simpson’s 3/8 rule and 384 equal parts in Boole’s rule by developing computer programs in C++ language. Error in the values of integral calculated by quadrature formulas is minimum when upper limit is in the neighborhood of zero and lower limit is -1. Accuracy of the quadrature formulas has been found in the order- Simpson’s three-eighth rule > Simpson’s one-third rule > Boole’s rule > Trapezoidal rule.