Given a function 
and two integers a and b. The task is to find the integrand of the given function from lower limit(a) to the upper limit(b) using Weedle’s Rule.
The given function is: 
Examples:
Input: a = 0, b = 6
Output: 1.373448Input: a = 10, b = 13
Output: f(x) = 0.022897
Approach:
The integration of any function using Weedle’s Formula is given by:
=
where,
h =and i = [0, 6]
= 
and i = [0, 6] 
Below are the steps:
- Find the value of h from the above formula i.e., h =
. - Find the value from
to 
and calculate the value from 
to - Substitute the above values in Weedle’s Formula to find the integral value.
to 
and calculate the value from 
to 
Below is the implementation of the above approach:
C++
// C++ program to Implement Weedle's Rule#include <bits/stdc++.h>using namespace std;// A sample function f(x) = 1/(1+x^2)float y(float x){ float num = 1; float denom = 1.0 + x * x; return num / denom;}// Function to find the integral value// of f(x) with step size h, with// initial lower limit and upper limit// a and bfloat WeedleRule(float a, float b){ // Find step size h double h = (b - a) / 6; // To store the final sum float sum = 0; // Find sum using Weedle's Formula sum = sum + (((3 * h) / 10) * (y(a) + y(a + 2 * h) + 5 * y(a + h) + 6 * y(a + 3 * h) + y(a + 4 * h) + 5 * y(a + 5 * h) + y(a + 6 * h))); // Return the final sum return sum;}// Driver Codeint main(){ // lower limit and upper limit float a = 0, b = 6; // Function Call cout<< "f(x) = "<< fixed << WeedleRule(a, b); return 0;}// This code is contributed by shivanisinghss2110 |
C
// C program to Implement Weedle's Rule#include <math.h>#include <stdio.h>// A sample function f(x) = 1/(1+x^2)float y(float x){ float num = 1; float denom = 1.0 + x * x; return num / denom;}// Function to find the integral value// of f(x) with step size h, with// initial lower limit and upper limit// a and bfloat WeedleRule(float a, float b){ // Find step size h double h = (b - a) / 6; // To store the final sum float sum = 0; // Find sum using Weedle's Formula sum = sum + (((3 * h) / 10) * (y(a) + y(a + 2 * h) + 5 * y(a + h) + 6 * y(a + 3 * h) + y(a + 4 * h) + 5 * y(a + 5 * h) + y(a + 6 * h))); // Return the final sum return sum;}// Driver Codeint main(){ // lower limit and upper limit float a = 0, b = 6; // Function Call printf("f(x) = %f", WeedleRule(a, b)); return 0;} |
Java
// Java program to Implement Weedle's Ruleimport java.util.*;class GFG{ // A sample function f(x) = 1/(1+x^2) static float y(float x) { float num = 1; float denom = (float)1.0 + x * x; return num / denom; } // Function to find the integral value // of f(x) with step size h, with // initial lower limit and upper limit // a and b static float WeedleRule(float a, float b) { // Find step size h float h = (b - a) / 6; // To store the final sum float sum = 0; // Find sum using Weedle's Formula sum = sum + (((3 * h) / 10) * (y(a) + y(a + 2 * h) + 5 * y(a + h) + 6 * y(a + 3 * h) + y(a + 4 * h) + 5 * y(a + 5 * h) + y(a + 6 * h))); // Return the final sum return sum; } // Driver Code public static void main(String args[]) { // lower limit and upper limit float a = 0, b = 6; // Function Call float num=WeedleRule(a, b); System.out.format("f(x) = "+"%.6f", num); }}// This code is contributed by AbhiThakur |
Python3
# Python3 program to Implement Weedle's Rule# A sample function f(x) = 1/(1+x^2)def y(x): num = 1; denom = float(1.0 + x * x); return num / denom;# Function to find the integral value# of f(x) with step size h, with# initial lower limit and upper limit# a and bdef WeedleRule(a, b): # Find step size h h = (b - a) / 6; # To store the final sum sum = 0; # Find sum using Weedle's Formula sum = sum + (((3 * h) / 10) * (y(a) + y(a + 2 * h) + 5 * y(a + h) + 6 * y(a + 3 * h) + y(a + 4 * h) + 5 * y(a + 5 * h) + y(a + 6 * h))); # Return the final sum return sum;# Driver Codeif __name__ == '__main__': # lower limit and upper limit a = 0; b = 6; # Function Call num = WeedleRule(a, b); print("f(x) = {0:.6f}".format(num));# This code is contributed by sapnasingh4991 |
C#
// C# program to Implement Weedle's Ruleusing System;class GFG{ // A sample function f(x) = 1/(1+x^2) static float y(float x) { float num = 1; float denom = (float)1.0 + x * x; return num / denom; } // Function to find the integral value // of f(x) with step size h, with // initial lower limit and upper limit // a and b static float WeedleRule(float a, float b) { // Find step size h float h = (b - a) / 6; // To store the final sum float sum = 0; // Find sum using Weedle's Formula sum = sum + (((3 * h) / 10) * (y(a) + y(a + 2 * h) + 5 * y(a + h) + 6 * y(a + 3 * h) + y(a + 4 * h) + 5 * y(a + 5 * h) + y(a + 6 * h))); // Return the final sum return sum; } // Driver Code public static void Main() { // lower limit and upper limit float a = 0, b = 6; // Function Call float num=WeedleRule(a, b); Console.Write("f(x) = "+num); }}// This code is contributed by AbhiThakur |
Javascript
<script>// Javascript program to Implement Weedle's Rule// A sample function f(x) = 1/(1+x^2)function y(x){ let num = 1; let denom = 1.0 + x * x; return num / denom;} // Function to find the integral value// of f(x) with step size h, with// initial lower limit and upper limit// a and bfunction WeedleRule(a, b){ // Find step size h let h = (b - a) / 6; // To store the final sum let sum = 0; // Find sum using Weedle's Formula sum = sum + (((3 * h) / 10) * (y(a) + y(a + 2 * h) + 5 * y(a + h) + 6 * y(a + 3 * h) + y(a + 4 * h) + 5 * y(a + 5 * h) + y(a + 6 * h))); // Return the final sum return sum.toFixed(6);}// Driver code// lower limit and upper limitlet a = 0, b = 6;// Function Calllet num = WeedleRule(a, b);document.write("f(x) = " + num);// This code is contributed by divyeshrabadiya07</script> |
Output:
f(x) = 1.373448
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