added simpsons rule in c++ and java (#1828)

Simpsons_rule/Simpsons_Rule.cpp

@@ -0,0 +1,51 @@
+//Simpson's Rule in c++
+//It is used to calculate numerical approximation of definite integral
+//In this rule, number of intervals must be EVEN
+
+#include <iostream>
+using namespace std;
+
+//Function to calculate f(x) where f(x) = x * x
+float func(float x){
+    return x*x;
+}
+
+//Function to calculate approximate integral
+float simpsons (float lb, float ub, int n){
+    float h = (ub - lb) / n;
+    float result = 0;
+    for (int i = 0; i <= n; i++){
+        if(i == 0 || i == n)
+            result = result + func(lb + i * h);
+        else if( i % 2 != 0)
+            result = result + 4 * func(lb + i * h);
+        else
+            result = result + 2 * func(lb + i * h);
+    }
+    result = result * (h / 3);
+    return result;
+}
+
+int main() {
+    float lower_limit, upper_limit, output;
+    int intervals;
+    cout << "Enter lower limit = ";
+    cin >> lower_limit;
+    cout << "Enter upper limit = ";
+    cin >> upper_limit;
+    cout<< "Enter number of intervals = ";
+    cin >> intervals;
+    if(intervals % 2 == 0){
+        output = simpsons(lower_limit, upper_limit, intervals);
+        cout << "Output = " << output;
+    }
+    else
+        cout << "Interval must be even.";
+    return 0;
+}
+
+//output -
+//Enter lower limit = 4
+//Enter upper limit = 5.2
+//Enter number of intervals = 6
+//Output = 25.536

Simpsons_rule/Simpsons_Rule.java

@@ -0,0 +1,57 @@
+//Simpson's Rule in java
+//It is used to calculate numerical approximation of definite integral
+//In this rule, number of intervals must be EVEN
+
+import java.util.Scanner;
+
+public class Main {
+
+    //Function to calculate f(x) where f(x) = x * x
+    static float func(float x){
+        return x * x;
+    }
+    //Function to calculate approximate integral
+    static float simpsons(float lb, float ub, int n){
+        float h = (ub - lb) / n;
+        float result = 0;
+        for (int i = 0; i <= n; i++){
+            if(i == 0 || i == n)
+                result += func(lb + i * h);
+            else if( i % 2 != 0)
+                result += 4 * func(lb + i * h);
+            else
+                result += 2 * func(lb + i * h);
+        }
+        result = result * (h / 3);
+        return result;
+
+    }
+
+    public static void main(String[] args) {
+        float lower_limit, upper_limit, output;
+        int intervals;
+        Scanner scanner= new Scanner(System.in);
+        System.out.println("Enter lower limit = ");
+        lower_limit = scanner.nextFloat();
+        System.out.println("Enter upper limit = ");
+        upper_limit = scanner.nextFloat();
+        System.out.println("Enter number of intervals = ");
+        intervals = scanner.nextInt();
+        if(intervals % 2 == 0){
+            output = simpsons(lower_limit, upper_limit, intervals);
+            System.out.println("Output = "+output);
+        }
+        else
+            System.out.println("Interval must be even.");
+    }
+}
+
+//output -
+//        Enter lower limit =
+//        4
+//        Enter upper limit =
+//        5.2
+//        Enter number of intervals =
+//        6
+//        Output = 25.535994
+