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MathGroup Archive 1992

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Yet another Integrate bug.

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Yet another Integrate bug.
  • From: bennett at phys.unca.edu (Chuck Bennett)
  • Date: Mon, 13 Apr 92 11:54:58 EDT

Here is another integral that Mathematica has trouble with.  Forget the
integral tables; you can do this one in your head. My comments are inserted
with #'s.

******************************************************

Mathematica 2.0 for SPARC
Copyright 1988-91 Wolfram Research, Inc.
 -- X11 windows graphics initialized -- 

# Integrate between the 1/e points:

In[1]:= Integrate[Exp[-2 Abs[x]], {x, -1, 1}] // Simplify

             -2
Out[1]= 1 - E     # Right.                 

# Now change variables and normalize ...

In[2]:= Solve[ c^2 Integrate[Exp[ -2 Abs[x] / x0], {x, -Infinity, Infinity}]==1, c]

                  1                  1
Out[2]= {{c -> --------}, {c -> -(--------)}}  # Right again.
               Sqrt[x0]           Sqrt[x0]

# Integrate between the 1/e points again...

In[3]:= Integrate[ (1/x0) Exp[-2 Abs[x] / x0], {x, -x0, x0}] // Simplify

                2
         -1    E
Out[3]= ---- + --   # Wrong.  Should be the same as Out[1]
           2   2
        2 E

# This function is symmetric about zero.  Get rid of the Abs funtion by
  integrating over positive x only:

In[4]:= Integrate[ 2 (1/x0) Exp[-2 x / x0], {x, 0, x0}] // Simplify

             -2
Out[4]= 1 - E    #  Now it gives the right answer.

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