Question

Is there a built-in routine for doing numerical integration in Mathematica given two lists of data as {x1, x2, ..., xn} and {y1, y2, ..., yn}?

I want to do something like trapezoidal integration or others. Doesn’t seem NIntegrate can do that. Of course I can write it on my own. Just think there are probably too many numerical integration schemes to try out, especially when I am eager to get it going.

Answer 1

Probably not what you have in mind, but you could set up an interpolation function:

dat = {#, Sin[#]} & /@ Range[0, 2*Pi, .1];

creates a list of data points (in the form of {x,y}).

fun = Interpolation[dat];

creates an interpolation functions (try plotting Plot[fun[x],{x,0,2*Pi}] to see what it is). You can then use NIntegrate:

NIntegrate[fun[x]^2, {x, 0, 2*Pi}]

However, if you really want to do it the matlab way that’s also possible.