Help with numerical integral

Hello everyone, I wrote this code to calculate the integral using the trapezoidal method, the code is correct. But now I want to plot a graph of this function where the x-axis I need to have h... how can I create parameter h using multiplication of 2... for example h is (b-a)/n, my next h is 2* h, next 4*h, next 6*, and so on. Can you help me with this?

clear all;

close all;

clc

e=0.1;

f=@(x)exp(x)./(1+x);

a=0.5;

b=1.1;

n=2;

h=(b-a)/n;

i=1:1:n-1;

S=f(a+i.*h);

tt = (h./2).*(f(a)+2.*sum(S)+f(b));

fprintf('The value of integration is %f\n', tt);

Answer 1

[Davide Masiello]

I guess this is what you're looking for

e=0.1;
f=@(x)exp(x)./(1+x);  
a=0.5; 
b=1.1; 
n=2;  
h=(b-a)/n;
i=1:1:n-1;
S=f(a+i.*h);
tt = (h./2).*(f(a)+2.*sum(S)+f(b));
fprintf('The value of integration is %f\n', tt);

The value of integration is 0.750379

hx = 0:2:n;
x = a+h*hx;
plot(hx,f(x),'-o')
xlabel('h')
ylabel('f(x)')

Of course it is a straight line here because you x goes only to 2*h.

if you increase the number of interval you'd get something like this

e=0.1;
f=@(x)exp(x)./(1+x);  
a=0.5; 
b=1.1; 
n=20;  
h=(b-a)/n;
i=1:1:n-1;
S=f(a+i.*h);
tt = (h./2).*(f(a)+2.*sum(S)+f(b));
fprintf('The value of integration is %f\n', tt);

The value of integration is 0.747541

hx = 0:2:n;
x = a+h*hx;
plot(hx,f(x),'-o')
xlabel('h')
ylabel('f(x)')

You may notice that the value of the integral has also changed (it is more accurate now).