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.
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Mathematica 2.0 for SPARC
Copyright 1988-91 Wolfram Research, Inc.
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# 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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