Substiuting variables within an integral
in [Mathematica]
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From: Eduardo M. A. M.Mendes on 27 Jul 2010 04:14 Hello I need to do a variable substitution within an integral in several different ways. I need Mathematica to rearrange the integral with the new variable definition without solving it. The resulting integral will be variations of Euler function. After seeing the resulting integral, I need Mathematica to actually solve it for me (that is, Mathematica needs to recognize that it is an Euler function). Can this be done? Many thanks Ed
From: Simon on 28 Jul 2010 02:53 Hi Ed, You can try working with the integrand and limits with out the integral. Something like f[x] Dt[x] && x0<x<x1 Then using replacement rules should just work. The total derivative Dt[] assumes that everything is a variable, so if you have any other parameters floating around you have to give them the attribute Constant. You can then get mathematica to check the form of the integrand - if it matches what you want, then integrate. Simon On Jul 27, 6:14 pm, "Eduardo M. A. M.Mendes" <emammen...(a)gmail.com> wrote: > Hello > > I need to do a variable substitution within an integral in several different > ways. I need Mathematica to rearrange the integral with the new variable > definition without solving it. The resulting integral will be variations > of Euler function. After seeing the resulting integral, I need Mathematica > to actually solve it for me (that is, Mathematica needs to recognize that it > is an Euler function). Can this be done? > > Many thanks > > Ed
From: Alexei Boulbitch on 28 Jul 2010 07:25 Hi, Ed, there is a package "Presentations" written by David Park that contains such operators and examples of how to do transformations of that sort. You may also do it without the package (though less beautiful), if your aim is simply to insert a new variable and see what is your integral looking like before its actual evaluation. As an example try the one below. Assume you are looking for the integral J=Integrate[func[y], y], where func[y] is a function in question: rule = {y -> q[x], \[DifferentialD]y -> D[q[x], x]*\[DifferentialD]x}; (* This is your transformation rule y=q[x], where q is some function *) underIntegral = func[y] \[DifferentialD]y (* This is the expression under the integral *) underIntegralTransformed = underIntegral /. rule (* This makes the transformation *) Integrate[Rest[underIntegralTransformed], x] (* This finally calculates the integral *) DifferentialD[y] func[y] DifferentialD[x] func[q[x]] \!\(\*SuperscriptBox["q", "\[Prime]", MultilineFunction->None]\)[x] \[Integral]func[q[x]] \!\(\*SuperscriptBox["q", "\[Prime]", MultilineFunction->None]\)[x] \[DifferentialD]x Be careful, the use of the operator Rest in the last line of commands is due to the necessity to remove DifferentialD[x], prior to substitute the expression into the operator Integrate. If you use a concrete transform instead y->q[x] (such as, for instance, y->x^2), the order of terms in underIntegralTransformed may become different, and you will need to use another operator to pick up the necessary terms or to remove the unnecessary one. Have fun, Alexei Hello I need to do a variable substitution within an integral in several different ways. I need Mathematica to rearrange the integral with the new variable definition without solving it. The resulting integral will be variations of Euler function. After seeing the resulting integral, I need Mathematica to actually solve it for me (that is, Mathematica needs to recognize that it is an Euler function). Can this be done? Many thanks Ed -- Alexei Boulbitch, Dr. habil. Senior Scientist Material Development IEE S.A. ZAE Weiergewan 11, rue Edmond Reuter L-5326 CONTERN Luxembourg Tel: +352 2454 2566 Fax: +352 2454 3566 Mobile: +49 (0) 151 52 40 66 44 e-mail: alexei.boulbitch(a)iee.lu www.iee.lu -- This e-mail may contain trade secrets or privileged, undisclosed or otherwise confidential information. If you are not the intended recipient and have received this e-mail in error, you are hereby notified that any review, copying or distribution of it is strictly prohibited. Please inform us immediately and destroy the original transmittal from your system. Thank you for your co-operation.
From: Eduardo M. A. M.Mendes on 29 Jul 2010 06:45 Hi Simon Since I am a newbie I wonder whether you would have a simple example. Many many thanks Ed -----Original Message----- From: Simon [mailto:simonjtyler(a)gmail.com] Sent: Wednesday, July 28, 2010 3:53 AM Subject: Re: Substiuting variables within an integral Hi Ed, You can try working with the integrand and limits with out the integral. Something like f[x] Dt[x] && x0<x<x1 Then using replacement rules should just work. The total derivative Dt[] assumes that everything is a variable, so if you have any other parameters floating around you have to give them the attribute Constant. You can then get mathematica to check the form of the integrand - if it matches what you want, then integrate. Simon On Jul 27, 6:14 pm, "Eduardo M. A. M.Mendes" <emammen...(a)gmail.com> wrote: > Hello > > I need to do a variable substitution within an integral in several different > ways. I need Mathematica to rearrange the integral with the new variable > definition without solving it. The resulting integral will be variations > of Euler function. After seeing the resulting integral, I need Mathematica > to actually solve it for me (that is, Mathematica needs to recognize that it > is an Euler function). Can this be done? > > Many thanks > > Ed
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