Solving for a function in an Integral
- To: mathgroup at smc.vnet.net
- Subject: [mg40797] Solving for a function in an Integral
- From: sclarke at lanl.gov (Steven Clarke)
- Date: Thu, 17 Apr 2003 23:17:21 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi I want to solve an equation of this form. f[x] = Integrate[Sin[x + m[t]],t] for m[t]. That is, I have a function f, in x, which is equal to a integral of a function in x and t, integrated over t. I have three questions. 1) Can this even be solved? 2) Does this kind of problem have a name (ie ODE, PDE, something else) so I can go look up a book on it something? 3) Can it be solved in Mathmatica, and if so, how? My first thought was to take the derivative of both sides with respect to t. That gives: f[x]/dt = Sin[x + m[t]] which I thought might be solvable with differential equations methods. But, f[x]/dt is 0, so all I get is a null solution. Any thoughts, suggestions, help would be greatly appreciated!