Fw: Integrate...

• To: mathgroup at smc.vnet.net
• Subject: [mg44304] Fw: Integrate...
• From: "Christos Argyropoulos M.D." <argchris at otenet.gr>
• Date: Wed, 5 Nov 2003 10:00:27 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
I think the problem goes deeper than simply mixing symbolic/numerical stuff.
Try symbolic integration of the original function to get:
In[9]:=
Integrate[Abs[ Cos[r] + Sin[r]], {r, a,b}]

Out[9]=
\!\(\((\(-a\) +
b)\)\ \((\(-\(\(Cos[a]\ \@\((Cos[a] + Sin[a])\)\^2 -
Sin[a]\ \@\((Cos[a] + Sin[a])\)\^2\)\/\(\((a -
b)\)\ \((Cos[a] +
Sin[a])\)\)\)\) + \(Cos[b]\ \@\((Cos[b] + Sin[b])\)\^2 -
\
Sin[b]\ \@\((Cos[b] + Sin[b])\)\^2\)\/\(\((a - b)\)\ \((Cos[b] +
Sin[b])\)\))\
\)\)

Simplification of the result gives:
\!\(\(\((Cos[a] - Sin[a])\)\ \@\(1 + Sin[2\ a]\)\)\/\(Cos[a] + Sin[a]\) + \
\(\((\(-Cos[b]\) + Sin[b])\)\ \@\(1 + Sin[2\ b]\)\)\/\(Cos[b] + Sin[b]\)\)
Results of the original, simplified versions and the numerical integration
agree for 0<=a<=2.35 and 0<=b<2.35
After they diverge dramatically. I suspect this is a bug somewhere inside
Integrate, but I do not have the guts to evaluate the
integral by hand to see, if the expression returned for symbolic a,b are
correct.

Any ideas?

Christos Argyropoulos
Patras Greece
----- Original Message -----
From: "Sampo Smolander" <sampo.smolander+news at helsinki.fi>
To: mathgroup at smc.vnet.net
Subject: [mg44304] Integrate...

> Does anybody know why
>
>    Integrate[Abs[1.0*Cos[r] + 1.0*Sin[r]], {r, 2.35, 2.36}]
>
> gives
>
>    -2.82839
>
> whereas without those 1.0's,
>
>    Integrate[Abs[Cos[r] + Sin[r]], {r, 2.35, 2.36}]
>
> gives the correct
>
>    0.000037373
>
> ?
>
> (I'm running Mathematica 4.1 on win98.)
>
> --
> Sampo Smolander ............... http://www.cs.helsinki.fi/u/ssmoland/
> Rolf Nevanlinna Institute, University of Helsinki ...................
>

```

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