# How to integrate a function which is only known at discrete points

I have an integration to do. I want to integrate.

$\int_0^\infty sin^2(2\pi t)f(t)dt$

where $f(t)$ takes values from an array in the form $\{t,f(t)\}$

The time steps in the array is 1.1s. Can you please suggest a method to do this? I tried using the Trapezoidal method for numerical integration but gave a bad approximation. Is there an easy method with inbuilt function or another method?

• Providing some code for f[t] or using Integrate might help :) – Öskå Aug 7 '14 at 9:55
• f[t] is just an array of points in the form {t,f(t)} and seems like integrate cannot perform integration over array. – jason Aug 7 '14 at 10:02
• Well, one might need the array right? And have you tried anything to say that it doesn't perform integration over an array? Please share. – Öskå Aug 7 '14 at 10:05
• Your function f(t) is discrete? – molekyla777 Aug 7 '14 at 10:12
• reference.wolfram.com/language/ref/Interpolation.html – george2079 Aug 7 '14 at 10:21

If you were to have, for example,

dt = .01;
tbl = Table[{t, Exp[Cos[t]]}, {t, 0, 10, dt}];

(that is, your $f(t)$ corresponds to my tbl) then another way is

Sin[2*Pi #1]^2 * #2 &,