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MathGroup Archive 2000

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Re: Mathematica gives bad integral ??

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24330] Re: Mathematica gives bad integral ??
  • From: zhl67 at my-deja.com
  • Date: Sun, 9 Jul 2000 04:52:39 -0400 (EDT)
  • References: <8k3n38$3pk@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

John,

I am confused with your post also: what you seem to have wished to do
is to perform a symbolic indefinite integration with Mathematica and
compare the result with existing text. As you have understood, there
are many equivalent forms for the same algebraic expression. Then you
seem to wish to confirm yourself with numerical tests. At this point,
however, there is some ambiguities in your description: at which
interval for x did you evaluate the DEFINITE integration? it is clear
that evaluating the numeric value of an indefinite integral is
meaningless: there is always an arbitrary integration constant in it
(which most symbolic algebra systems omit in their output).

I tested the same integration and get the following result:

In[1]:=Integrate[1/Sqrt[1-Sin[2x]],{x,0,Pi/8}]//N

Out[1]:=0.518675+0. I

In[2]:=NIntegrate[1/Sqrt[1-Sin[2x]],{x,0,Pi/8}]

Out[2]:=0.518675

In[3]:=Integrate[1/Sqrt[1-Sin[2x]],{x,0,Pi/16}]//N

Out[1]:=0.220268+0. I

In[2]:=NIntegrate[1/Sqrt[1-Sin[2x]],{x,0,Pi/16}]

Out[2]:=0.220268

Mathematica seems to give consistent result!

On the other hand, evaluating the difference of Schaum's result gives

(f[x_] is defined to be the Schaum's integral)

In[6]:=f[Pi/8]-f[0]

Out[6]:=0.518675

In[7]:=f[Pi/16]-f[0]

Out[7]:=0.220268

This also give the same result! (All these are with Ver 4.0)

L Zhao


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