quest3.java

import java.util.Scanner;
import java.io.*;
import java.lang.Math;

public class quest3 {

    static double Vm;
    static double F;
    static int N = 1000;

    public static void main(String args[]){

        Scanner scanner = new Scanner(System.in);
        printLine("Enter Vm: ");
        Vm = scanner.nextDouble();

        printLine("Enter F: ");
        F = scanner.nextDouble();

        double upperLimit = Math.PI/2;
        double lowerLimit = -Math.PI/2;

        double interval = (upperLimit - lowerLimit)/N;

        double integralSimps = Simpsons(upperLimit, lowerLimit, interval); 
        double integralTrapz = Trapezoidal(upperLimit, lowerLimit, interval); 
        printLine("Using Simpson's rule : " + integralSimps);      
        printLine("Using Trapezoidal rule : " + integralTrapz);      
        
    }

    public static double Ft(double t){
        return Vm * Math.sin((2 * Math.PI * F * t)); 
    }

    public static double Simpsons(double upperLimit, double lowerLimit, double interval){
        
        int i = 0;
        double sum = 0;
        while (i < N){
            i++;
            double t = lowerLimit + (i * interval);
            //even 
            if (i % 2 == 0){
                sum += 2 * Ft(t);
            }
            //odd
            else{
                sum += 4 * Ft(t);
            }
        }

        return (interval/3) * (sum + Ft(upperLimit) + Ft(lowerLimit));

    }


    public static double Trapezoidal(double upperLimit, double lowerLimit, double interval){

        double sum = (Ft(upperLimit) + Ft(lowerLimit))/2;

        int c = 1;

        while (c < N){
            double t = lowerLimit + (c * interval);
            sum += Ft(t);
            c++;
        }

        return interval * sum;
    }

    public static void print(String text){
        System.out.print(text);
    }

    public static void printLine(String text){
        System.out.println(text);
    }

}