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Solving an integral for an unknown function
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Mikael
Jan 22, 2012, 7:34:22 AM1/22/12
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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
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
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