How to resolve the algorithm Numerical integration step by step in the Pascal programming language

Published on 12 May 2024 09:40 PM
#Pascal

How to resolve the algorithm Numerical integration step by step in the Pascal programming language

Table of Contents

Problem Statement

Write functions to calculate the definite integral of a function ƒ(x) using all five of the following methods: Your functions should take in the upper and lower bounds (a and b), and the number of approximations to make in that range (n). Assume that your example already has a function that gives values for ƒ(x) . Simpson's method is defined by the following pseudo-code:

Demonstrate your function by showing the results for:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Numerical integration step by step in the Pascal programming language

Source code in the pascal programming language

function RectLeft(function f(x: real): real; xl, xr: real): real;
 begin
  RectLeft := f(xl)
 end;

function RectMid(function f(x: real): real; xl, xr: real) : real;
 begin
  RectMid := f((xl+xr)/2)
 end;

function RectRight(function f(x: real): real; xl, xr: real): real;
 begin
  RectRight := f(xr)
 end;

function Trapezium(function f(x: real): real; xl, xr: real): real;
 begin
  Trapezium := (f(xl) + f(xr))/2
 end;

function Simpson(function f(x: real): real; xl, xr: real): real;
 begin
  Simpson := (f(xl) + 4*f((xl+xr)/2) + f(xr))/6
 end;

function integrate(function method(function f(x: real): real; xl, xr: real): real;
                   function f(x: real): real;
                   a, b: real;
                   n: integer);
 var
  integral, h: real;
  k: integer;
 begin
  integral := 0;
  h := (b-a)/n;
  for k := 0 to n-1 do
   begin
    integral := integral + method(f, a + k*h, a + (k+1)*h)
   end;
  integrate := integral
 end;

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