integration limit notation
in [Math]
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From: cronusf on 24 Feb 2010 04:15 I'm looking at a book that solves a differential equation with integrating factor. In the end that get something like: L(x) = exp( int_^x()dx ) Note that they omit the lower limit of integration and just keep the upper limit of integration. What does this mean? Is this a shortcut where the lower integration limit is implied somehow (it would be 0 in the context of the problem).
From: The Qurqirish Dragon on 24 Feb 2010 14:55 On Feb 24, 2:15 pm, "cron...(a)gmail.com" <cron...(a)gmail.com> wrote: > I'm looking at a book that solves a differential equation with integrating factor. In the end that get something like: > > L(x) = exp( int_^x()dx ) > > Note that they omit the lower limit of integration and just keep the upper limit of integration. What does this mean? Is this a shortcut where the lower integration limit is implied somehow (it would be 0 in the context of the problem). I would guess this notation is to show that the integrating factor is the exponential of an integral- but they don't want to have to worry about the "arbitrary constant" you get from such an action. The lower limit of integration can be chosen to be anything (since this value can be absorbed into the general constant that certainly appears in the solution of the DE in the text).
From: W^3 on 24 Feb 2010 18:03 In article <1639156091.263730.1267038939707.JavaMail.root(a)gallium.mathforum.org>, "cronusf(a)gmail.com" <cronusf(a)gmail.com> wrote: > I'm looking at a book that solves a differential equation with integrating > factor. In the end that get something like: > > L(x) = exp( int_^x()dx ) If the upper limit is x, then the dx needs to be changed. > Note that they omit the lower limit of integration and just keep the upper > limit of integration. What does this mean? Is this a shortcut where the > lower integration limit is implied somehow (it would be 0 in the context of > the problem).
From: mary on 24 Feb 2010 18:09 <cronusf(a)gmail.com> wrote in message news:1639156091.263730.1267038939707.JavaMail.root(a)gallium.mathforum.org... > I'm looking at a book that solves a differential equation with integrating > factor. In the end that get something like: > > L(x) = exp( int_^x()dx ) > > Note that they omit the lower limit of integration and just keep the upper > limit of integration. What does this mean? Is this a shortcut where the > lower integration limit is implied somehow (it would be 0 in the context > of the problem). equation is wrong or malformed, the integral part of it. no integrand, no upper limit, no lower limit, and what is ^x ?? guessing => integral ( a^x )dx from 0 to n
From: W. Dale Hall on 24 Feb 2010 18:15
mary wrote: > <cronusf(a)gmail.com> wrote in message > news:1639156091.263730.1267038939707.JavaMail.root(a)gallium.mathforum.org... >> I'm looking at a book that solves a differential equation with integrating >> factor. In the end that get something like: >> >> L(x) = exp( int_^x()dx ) >> >> Note that they omit the lower limit of integration and just keep the upper >> limit of integration. What does this mean? Is this a shortcut where the >> lower integration limit is implied somehow (it would be 0 in the context >> of the problem). > > > equation is wrong or malformed, the integral part of it. > > no integrand, no upper limit, no lower limit, and what is ^x ?? > > guessing => integral ( a^x )dx from 0 to n > > That ^x just represents the upper limit of the integral inside the exponential. The integrand is determined by the problem to be solved, but yes it should be there if only to provide an example. The OPs question was about what happened to the lower limit of integration. |