Re: Solving for a function in an Integral
- To: mathgroup at smc.vnet.net
- Subject: [mg40804] Re: [mg40797] Solving for a function in an Integral
- From: Bobby Treat <drmajorbob+MathGroup3528 at mailblocks.com>
- Date: Sat, 19 Apr 2003 22:59:01 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Without limits for the integral, I'm not sure what the equation means at all. Usually we would think of the indefinite integral as a function of x and t, with an arbitrary constant. The constant could depend on anything but t so -- for instance -- the "constant" could be f[x]. I think you need to decide clearly what you're trying to do. Bobby -----Original Message----- From: Steven Clarke <sclarke at lanl.gov> To: mathgroup at smc.vnet.net Subject: [mg40804] [mg40797] Solving for a function in an Integral 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!