An Argument Problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg91722] An Argument Problem*From*: Mr Ajit Sen <senra99 at yahoo.co.uk>*Date*: Sat, 6 Sep 2008 02:09:07 -0400 (EDT)*Reply-to*: senra99 at yahoo.co.uk

Dear Mathgroup, I am trying to numerically integrate a function of several variables w.r.t. its last variable. As NIntegrate won't work, I decided to use Simpson's 1/3 rule. Below is my attempt for a function of 2 variables (using Mathematica 6.0): Simpson[F_, a_, b_, n_?EvenQ] := Module[{h, evens, odds}, h = (b - a)/n; evens = Table[a + i h, {i, 2, n - 2, 2}]; odds = Table[a + i h, {i, 1, n - 1, 2}]; h/3 {F[x, a], F[x, b], 4 F[x, #] & /@ odds, 2 F[x, #] & /@ evens} // Flatten // Total] // Simplify // N This works OK & returns a function of x. My query is how to make Simpson give a function of whatever the fist argument of F is. Thus, if F= F[r,t]= , Simpson would integrate w.r.t. t & give a function of r (without my having to change the x's into r's). Basically, I can't suss out how to pass the first argument of F inside the module. Thanks for any help. Regards. Ajit