Solving an integral for an unknown function
- To: mathgroup at smc.vnet.net
- Subject: [mg124528] Solving an integral for an unknown function
- From: Mikael <mikaen.anderson.1969 at gmail.com>
- Date: Sun, 22 Jan 2012 07:28:49 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Dear All,
I wonder if anyone could let me know if there is a general solution to the following problem in Mathematica.
Suppose the functions g[u,w] and h[w] are known. I want to find a function f[u] such that
Integrate[g[u,w]*f[u],{u,0,1}]=h[w].
In addition I know that
Integrate[f[u],{u,0,1}]=2
and
Integrate[u*f[u],{u,0,1}]=1.
Is it possible to solve the above for the unknown function f[u]? Of course there might be several solutions but I would be happy to find one.
Many thanks in advance for any suggestions.
Mikael