Interpolation for numerical integration

[kaniello]

Hallo,
$\Gamma$(t) is a function that i can know only at dicrete points and appears in this integral:
$\int$$\Gamma$(t) * tan ($\Gamma(t)$*t + $\varphi$)
My question is now, which could be the best interpolation of $\Gamma$(t) that would allopw an exact integration?
Thank you very much in advance

 

[HallsofIvy]

What do you mean by an "exact integration"?

Simpson's rule- http://en.wikipedia.org/wiki/Simpson's_rule - is probably the best of the elementary numerical integration methods.

 

[kaniello]

Simpon's rule is definitely a good option. What I was looking for is the following: imagine that in the place of $\Gamma(t)$ you have an approximation, like a Taylor series, or sine series or whatever, that would allow an analytical integration of this approximated expression.