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+//Example 7.8
+
+clc
+clear
+
+function [I] = trap (fun,a,b,n)
+// Integrate the function over the interval using Trapezoidal Formula
+// trap (fun,a,b,n)
+// fun - function to be integrated
+// a - lower limit of integration
+// b - upper limit of integration
+// n - No. of times trapezoidal rule needs to be performed
+
+N = n + 1;  // N - total no. of points
+h = (b-a) / (N-1);
+x = linspace(a,b,N);
+y = fun(x);
+
+sum1 = y(1) + 2 * sum(y(2:N-1)) + y(N);
+I = h * sum1 / 2;                   // Trapezoidal Integral Value
+endfunction
+
+function [I] = simp13 (fun,a,b,n)
+// Integrate the function over the interval using Simpson's 1/3rd rule
+// simp13 (fun,a,b,n)
+// fun - function to be integrated
+// a - lower limit of integration
+// b - upper limit of integration
+// n - No. of times simpson's 1/3rd rule needs to be performed
+
+N = 2 * n + 1;      // N - total no. of points
+h = (b-a) / (N-1);
+x = linspace(a,b,N);
+y = fun(x);
+
+sum1 = y(1) + 4 * sum(y(2:2:N-1)) + 2 * sum(y(3:2:N-2)) + y(N);
+I = h* sum1 / 3;                    // Simpson's 1/3rd Integral Value
+endfunction
+
+function [f] = fun1(x)
+    f = 1 ./(1+x^2);
+endfunction
+
+
+n = 4;
+ntrap = n;
+ns13 = n/2;
+I = [trap(fun1,0,1,ntrap); simp13(fun1,0,1,ns13)];
+I = round(I*10^4)/10^4;
+true = intg(0,1,fun1);
+
+disp(I(1),"y_trap = ")
+disp(I(2),"y_simp13 = ")
+disp(I(2)*4,"Approx pi = ")