performing integration using quadgk

I would like to perform integration of y w.r.to x wherein I know the limits a, b (lower and upper limits for x) as well as the arrays x and y (n x 1 size each) using quadgk.

For example, see the below code:

x=0.0:0.1:5;
y=exp(x);

int_exact = exp(5) - exp(0);
int_trapz = trapz(x,y);
int_quadgk = quadgk(@integrand,0,5);

How can I code to get int_quadgk using the x and y arrays ONLY and NOT the function exp(x)? That is, I know only x and y arrays and NOT the function from which they were arrived at.

Please help.

Thanks

Answer 1

[Walter Roberson]

quadgk is strictly for the case where you can pass in a function. trapz() is suitable for numeric integration over a fixed set of data.

[Ramakrishna]

As you can see, there is considerable error between the exact value (int_exact) and that obtained using trapz (int_trapz). Hence, I plan to use quadgk to minimise the error.

Alternatively, is there a different way to numerically evaluate the integral with reduced / no error?

Thanks

[Walter Roberson]

http://www.mathworks.com/matlabcentral/fileexchange/28726-simpsons-rule-integration