Trapezoidal Rule Algorithm

The trapezoidal rule, informally the trapezoid rule, is a technique for numerical integration that approximates the definite integral of a function by approximating the region under its graph as a trapezoid and calculating that trapezoid's area. In practice the interval of integration is typically partitioned into many smaller subintervals, with the trapezoidal rule applied to each and the results summed, a chained or composite form that becomes more accurate as the number of subintervals increases; the rule can also be understood as the average of the left and right Riemann sums.