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MathGroup Archive 2000

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Re: Simplification During Integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21472] Re: [mg21391] Simplification During Integration
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Tue, 11 Jan 2000 04:17:51 -0500 (EST)
  • References: <84s751$q6r@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Andrzej:

With
Integrate[Factor[y], t]

Sin[g]^2*(2*t*Cos[g/2]^3*Sec[g]*Sin[g/2] -
   Cos[g/2]*Sec[g]*Sin[g/2]^3*Sin[2*t])*Tan[g]^2

we still have some changes.
But we can use


Integrate[y /. p : _[g] :> A[p], t] /. A[p_] -> p

(1*Sin[g]^2*Sin[2*t]*(Sin[g] - Tan[g])*Tan[g]^2)/4 +
  (1*t*Sin[g]^2*Tan[g]^2*(Sin[g] + Tan[g]))/2


Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565



"Andrzej Kozlowski" <andrzej at tuins.ac.jp> wrote in message
news:84s751$q6r at smc.vnet.net...
> This  happen only in rather special cases, usually involving triginometric
> functions. If you prefer you can make Mathematica factor out the common
> terms, e.g. :
>
> In[14]:=
> Integrate[Factor[y], t]
> Out[14]=
>       2          g 3            g
> Sin[g]  (2 t Cos[-]  Sec[g] Sin[-] -
>                  2              2
>
>         g             g 3                 2
>     Cos[-] Sec[g] Sin[-]  Sin[2 t]) Tan[g]
>         2             2
>
> You can't however in general stop Mathematica transforming the remaining
> terms (even those that do not depend on the variable of integration) since
> it is often the case that one can  reduce an integral to a form that can
be
> integrated only by performing such transformations.
>
>
> > From: Joel Storch <jstorch at earthlink.net>
To: mathgroup at smc.vnet.net
> > Organization: EarthLink Network, Inc.
> > Date: Mon, 3 Jan 2000 03:12:24 -0500 (EST)
> > To: mathgroup at smc.vnet.net
> > Subject: [mg21472] [mg21391] Simplification During Integration
> >
> > In performing a definite or indefinite integral, Mathematica performs
> > transformations on parameters which are not dependent upon the variable
> > of integration. How do I supress this type of behavior ?
> >
> > Example: Consider the two term expression
> >
> > y=Tan[g]^2 Sin[g]^3 Cos[t]^2 + Tan[g]^3 Sin[g]^2 Sin[t]^2
> >
> > Integrate[y,{t,0,a}] results in an expression in which the
> > trigonometric functions of g have been transformed. I would
> > expect Mathematica to recognize that these factors are independent of t
> > and simply "pull them out" from the integral. Integrating either of the

> > terms separately, does not result in these type of transformations.
> >
>
>




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