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In the branch of mathematics known as real analysis, the Riemann integral â„›, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. ... In mathematics, the integral of a function of one real variable can be regarded as the area of a plane region bounded by the graph of that function. ... In mathematics and physics, there are various distinct notions that are referred to under the name of integrable systems. ... Image File history File links Disambig_gray. ...
In mathematics, an integrablefunction is a function whose integral exists.
Unless specifically stated, the integral in question is usually the Lebesgue integral.
This is especially useful in quantum mechanics as wave functions must be square integrable over all space if a physically possible solution is to be obtained from the theory.
In mathematics and physics, an integrable system refers to a system of partial differential equations that may be integrated to obtain the solutions to the equations.
A completely integrable system is a system that has n degrees of freedom, n constants of motion, and whose constants of motion are in involution: that is, the Poisson bracket between each pair of constants of motion vanishes.
The actions are the constants of motion, and all motion occurs on the surface of a torus, known as the invariant torus.
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