 Trapezoid Rule Using Distinct Points - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: HP Prime Software Library (/forum-15.html) +--- Thread: Trapezoid Rule Using Distinct Points (/thread-13044.html) Trapezoid Rule Using Distinct Points - Eddie W. Shore - 05-30-2019 12:12 PM Blog Link: http://edspi31415.blogspot.com/2019/05/hp-prime-and-hp-17bii-trapezoid-rule.html We can estimate the area of any surface by the use of sums and integral. In calculus, we usually are given a function f(x), but here we are using measurements from one end to the other at various intervals. Technically, the intervals between each measurement do not have to be equal length. However, having intervals of equal length makes things a lot easier, and in this blog entry, we assume they are. We have various methods to estimate the area. One of the easiest ways is the Trapezoid Rule: Area ≈ h/2 * ( y_1 + y_n + 2 * Σ( y_k , k, 2, n-1 ) ) Where: h = interval length y_k = length of each measurement, there are n measurements y_1 and y_n: measurement of lengths at each end, respectively Another rule to estimate area is the Simpson's Rule: Area ≈ h/3 ( y_0 + y_n + 4 * Σ( y_k, k, 1, n-1, 2) + 2 * Σ( y_k, k, 2, n-2, 2) ) The program presented here uses the Trapezoid Rule. HP Prime Program AREAHGT Two arguments: h, a list of measurements Code: ``` EXPORT AREAHGT(h, ms) BEGIN // h:  increment between measurements // ms: list of measurements // 2019-05-09 EWS LOCAL k,n:=SIZE(ms); RETURN h/2 * (ms(1) + ms(n) + 2 * Σ( ms(k), k, 2, n-1 )); END;```