Applying lists to FindRoot of a NIntegrate function

*To*: mathgroup at smc.vnet.net*Subject*: [mg101284] Applying lists to FindRoot of a NIntegrate function*From*: Christian Schneider <kofferpc at gmx.net>*Date*: Tue, 30 Jun 2009 06:31:56 -0400 (EDT)

Dear members of the mathgroup email group, I have serious difficulties in solving the following problem in Mathematica (v.6) and would very appreciate it if anyone could give me a helping hand with that. To start with, I have a list of data points {{x[[i]],y[[i]]}}. Also, I have the function W. W consists of two single functions f[r] and g[r, x, a]: f[r_] = r^2+r+2/(r^2+r) g[r_, x_, a_] = Exp[a*Exp[-x*r]] W := NIntegrate[f[r]*g[r, x, a], {r, 0.1, 100}] What I have given for every pair of data is W[x[[i]]] == y[[i]] (see the list of data points). What I do not have is the corresponding value of a[[i]]. So, I want to use FindRoot to give me the value of a[[i]] for each of my data pairs {x[[i]],y[[i]]}. Although I have found many examples quite similar to this problem, I have been unable to adjust those to work in my case. I would be very grateful if somebody could provide me with the proper syntax for this. Thanks very much in advance, Chris