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- import java.util.Arrays;
- import java.util.List;
- public class Start {
- public static void main(String[] args) {
- doMidpoint();
- doTrapezoid();
- doSimpsons();
- }
- private static void doMidpoint() {
- List<Integer> subDivisions = Arrays.asList(10);
- double a = 0;
- double b = 2;
- System.out.println("Midpoint Rule:");
- for(int n : subDivisions) {
- double h = (b-a)/n;
- double answer = 0;
- for(double i = a; i <= (b-h); i+=h) {
- answer = answer + MidF((i+(i+h))/2);
- }
- answer = answer * h;
- double second = (1/Math.sqrt(2 * Math.PI));
- answer = answer * second;
- answer = answer + 0.5;
- System.out.println("SubDivision " + n + " = " + answer);
- }
- System.out.println("");
- }
- private static double MidF(double x) {
- double power = (-1 * Math.pow(x, 2))/2;
- return Math.exp(power);
- }
- private static void doTrapezoid() {
- List<Integer> subDivisions = Arrays.asList(10);
- double a = 0;
- double b = 2;
- System.out.println("Trapezoid Rule:");
- for(int n : subDivisions) {
- double h = (b-a)/n;
- double answer = (MidF(a) + MidF(b))/2;
- for(int k = 1; k < n; k++) {
- answer += MidF((a + (k*h)));
- }
- answer *= h;
- double second = (1/Math.sqrt(2 * Math.PI));
- answer = answer * second;
- answer = answer + 0.5;
- System.out.println("SubDivision " + n + " = " + answer);
- }
- System.out.println("");
- }
- private static void doSimpsons() {
- List<Integer> subDivisions = Arrays.asList(10);
- double a = 0;
- double b = 2;
- System.out.println("Simpsons Rule:");
- for(int n : subDivisions) {
- double h = (b-a)/n;
- double answer = MidF(a) + MidF(b);
- for(int k = 1; k < n; k+=2) {
- answer += (4 * MidF((a + (k*h))));
- }
- for(int k = 2; k < (n-1); k+=2) {
- answer += (2 * MidF((a + (k*h))));
- }
- answer = (answer * h)/3;
- double second = (1/Math.sqrt(2 * Math.PI));
- answer = answer * second;
- answer = answer + 0.5;
- System.out.println("SubDivision " + n + " = " + answer);
- }
- }
- }
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