Added Trapezoidal Rule

src/com/jwetherell/algorithms/mathematics/TrapezoidalRule.java

@@ -0,0 +1,74 @@
+
+import java.util.*;
+import java.lang.*;
+
+public class TrapezoidalRule {
+
+	public static void main(String[] args) {
+
+		int a,b;
+		int d,n;
+		int h;
+		int x,y;
+		int s=0;
+		int sum;
+		int Area;
+
+		Scanner sc= new Scanner(System.in);
+
+		//Taking input of the Polynomial:
+
+		System.out.print("Enter the Degree of Polynomial : ");
+		d =sc.nextInt();
+		System.out.print("\n");
+		int coef[]=new int[d+1];
+		System.out.print("Enter the Coefficients : ");
+		for(int i=d;i>=0;i--){
+			coef[i]=sc.nextInt();
+		}
+		System.out.print("\n");
+
+		System.out.print("Enter the Lower Limit : ");
+		a=sc.nextInt();
+		System.out.print("Enter the Upper Limit : ");
+		b=sc.nextInt();
+		System.out.print("Enter the number of partitions : ");
+		n=sc.nextInt();
+
+		//Printing the entered Polynomial:
+
+		System.out.print("The Polynomial you Entered is f(x)= ");
+		for(int i=d;i>0;i--)
+		{
+		System.out.print(coef[i]+"x^"+i+" + ");
+
+		}
+		System.out.print(coef[0]+"\n");
+		System.out.println("Upper Limit : "+b+", Lower LImit : "+a+", Partitions : "+n);
+
+		//Calculation
+
+		h=(b-a)/n;
+		int yarr[]= new int[n+1];
+		for(int i=0;i<=n;i++){
+			s=0;
+			x=a+i*h;
+
+			for(int j=0;j<=n;j++){
+				for(int k=0;k<=d;k++){
+				s+=(int) (coef[j]*Math.pow(x,k));
+				}
+			}
+			yarr[i]=s;
+
+		}
+		sum=yarr[0];
+		for(int i=1;i<=n-1;i++){
+			yarr[i]=2*yarr[i];
+			sum+=yarr[i];
+		}
+		sum+=yarr[n];
+		Area= (h*sum)/2;
+		System.out.println("The Area under the Given curve : "+Area);
+	}
+}