Finding Integrand using Weedle's Rule Last Updated : 22 Dec, 2022 Comments Improve Suggest changes Like Article Like Report Given a function f(x) 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: f(x) = \frac{1}{(1+x)^2} Examples: Input: a = 0, b = 6 Output: 1.373448 Input: a = 10, b = 13 Output: f(x) = 0.022897 Approach: The integration of any function f(x) using Weedle's Formula is given by: \int_{a}^{b} f(x) dx = \frac{3}{10} h (f_1 + 5f_2 + f_3 + 6f_4 + f_5 + 5f_6 + f_7) where, h = \frac{(b-a)}{6} f_i = f(x_i) and i = [0, 6] x_1 = a x_2 = x_1 + h x_3 = x_1 + 2h x_4 = x_1 + 3h x_5 = x_1 + 4h x_6 = x_1 + 5h Below are the steps: Find the value of h from the above formula i.e., h = \frac{(b-a)}{6} .Find the value from x_1 to x_7 and calculate the value from f(x_1) to f(x_7) Substitute the above values in Weedle's Formula to find the integral value. 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 b float 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 Code int 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 b float 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 Code int 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 Rule import 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 b def 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 Code if __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 Rule using 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 b function 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 limit let a = 0, b = 6; // Function Call let num = WeedleRule(a, b); document.write("f(x) = " + num); // This code is contributed by divyeshrabadiya07 </script> Output: f(x) = 1.373448 Comment More infoAdvertise with us Next Article Finding Integrand using Weedle's Rule kartik Follow Improve Article Tags : Mathematical DSA Practice Tags : Mathematical Similar Reads Program for finding the Integral of a given function using Boole's Rule Given a function, f(x), tabulated at points x_i equally spaced by h=x_{i+1} - x_i such that f_1 = f(x_1) f_2=f(x_2) .....and so on The upper and lower limits a, b correspond to which the integral needs to be found, the task is to find the integral value of the given equation f(x).Examples: Input: a 8 min read Program to implement Simpson's 3/8 rule Write a program to implement Simpson's 3/8 rule.The Simpson's 3/8 rule was developed by Thomas Simpson. 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