The following code
clc; input(" Please press 'Enter' to continue. ","s"); % clc; disp(" "); % W$=[" Needs four inputs: the order, the lower and upper"]; W$=[W$,[" bounds, and the integrand function type.\n"]]; X$=[" To add 1% noise, add 0.5 to the integer function number, e.g. 2.5.\n"]; disp(W$); disp("\n The integrand function types are:\n"); disp(" 1. x^ord"); disp(" 2. exp(ord*x)"); disp(" 3. exp(ord*x^2)"); disp(" 4. sin(ord*x)"); disp(" 5. 1/(ord^2 + x^2)\n"); disp(X$); % disp(" "); ord=input(" Enter the order: "); % xl=input(" Enter the lower limit: "); xu=input(" Enter the upper limit: "); if xuProduces the following output
Please press 'Enter' to continue. Needs four inputs: the order, the lower and upper bounds, and the integrand function type. The integrand function types are: 1. x^ord 2. exp(ord*x) 3. exp(ord*x^2) 4. sin(ord*x) 5. 1/(ord^2 + x^2) To add 1% noise, add 0.5 to the integer function number, e.g. 2.5. Enter the order: 1 Enter the lower limit: 2 Enter the upper limit: 5 Enter the integrand function type: 2 e^(1*x) on (2,5) #.##e-014 is just numerical noise. Points = 2 I = 2.3370e+02 % RelErr = 6.6e+01 Points = 3 I = 1.4413e+02 % RelErr = 2.2e+00 Points = 4 I = 1.4244e+02 % RelErr = 1.0e+00 Points = 5 I = 1.4106e+02 % RelErr = 2.9e-02 Points = 6 I = 1.4105e+02 % RelErr = 1.6e-02 Points = 7 I = 1.4102e+02 % RelErr = 3.1e-04 Points = 8 I = 1.4102e+02 % RelErr = 1.9e-04 Points = 9 I = 1.4102e+02 % RelErr = 2.6e-06 Points = 10 I = 1.4102e+02 % RelErr = 1.7e-06 Points = 11 I = 1.4102e+02 % RelErr = 1.6e-08 Points = 12 I = 1.4102e+02 % RelErr = 2.0e-07 Points = 13 I = 1.4102e+02 % RelErr = 7.8e-08 Points = 14 I = 1.4102e+02 % RelErr = 3.4e-08 Points = 15 I = 1.4102e+02 % RelErr = 1.6e-08 Points = 16 I = 1.4102e+02 % RelErr = 7.6e-09 Points = 17 I = 1.4102e+02 % RelErr = 3.9e-09 Points = 18 I = 1.4102e+02 % RelErr = 2.1e-09 Points = 19 I = 1.4102e+02 % RelErr = 1.1e-09 Points = 20 I = 1.4102e+02 % RelErr = 6.5e-10 Points = 21 I = 1.4102e+02 % RelErr = 3.8e-10 Points = 22 I = 1.4102e+02 % RelErr = 2.3e-10 Points = 23 I = 1.4102e+02 % RelErr = 1.4e-10 Points = 24 I = 1.4102e+02 % RelErr = 8.9e-11 Points = 25 I = 1.4102e+02 % RelErr = 5.7e-11 Points = 26 I = 1.4102e+02 % RelErr = 3.7e-11 Points = 27 I = 1.4102e+02 % RelErr = 2.5e-11 Points = 28 I = 1.4102e+02 % RelErr = 1.7e-11 Points = 29 I = 1.4102e+02 % RelErr = 1.1e-11 Points = 30 I = 1.4102e+02 % RelErr = 7.9e-12 Points = 31 I = 1.4102e+02 % RelErr = 5.6e-12 Points = 32 I = 1.4102e+02 % RelErr = 3.9e-12 Points = 33 I = 1.4102e+02 % RelErr = 2.8e-12 Points = 34 I = 1.4102e+02 % RelErr = 2.1e-12 Points = 35 I = 1.4102e+02 % RelErr = 1.5e-12 Points = 36 I = 1.4102e+02 % RelErr = 1.1e-12 Points = 37 I = 1.4102e+02 % RelErr = 8.0e-13 Points = 38 I = 1.4102e+02 % RelErr = 6.2e-13 Points = 39 I = 1.4102e+02 % RelErr = 4.7e-13 Points = 50 I = 1.4102e+02 % RelErr = 2.2e-14 Points = 100 I = 1.4102e+02 % RelErr = 0.0e+00 Points = 200 I = 1.4102e+02 % RelErr = -2.2e-14 Points = 500 I = 1.4102e+02 % RelErr = 0.0e+00 Points = 1000 I = 1.4102e+02 % RelErr = -2.2e-14 Points = 10000 I = 1.4102e+02 % RelErr = 0.0e+00 Points = 100000 I = 1.4102e+02 % RelErr = -2.2e-14
Package: integration