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Re: Mathematica not considering an assumption

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82669] Re: Mathematica not considering an assumption
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Sun, 28 Oct 2007 03:57:28 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <ffv36o$bf0$1@smc.vnet.net>

matematica65 at gmail.com wrote:

> Assuming[a < 0,Integrate[x^a, {x, 5, 6}]}]
------------------------------------------^
Syntax error: extraneous curly bracket.

> This Integral, for a = -1, is equal to Log(6/5)
> 
> Why doesn't Mathematica report it?

Usually, functions like *Integrate* return the most general solution, 
solution applicable in most cases, without returning any constants of 
integration or restrictions on the domain or special cases. For 
instance, integrating 1/x just return the antiderivative Log[x], which 
obviously does not work for x == 0 (or x < 0 if we restrict ourself to 
the reals).

In[1]:= Integrate[1/x, x]

Out[1]= Log[x]

In[2]:= Assuming[a < 0, Integrate[x^a, {x, 5, 6}]]

Out[2]= (-5^(1 + a) + 6^(1 + a))/(1 + a)

In[3]:= Limit[%, a -> -1, Direction -> -1]

Out[3]= Log[6/5]

In[4]:= Limit[%, a -> -1, Direction -> +1]

Out[4]= Log[6/5]

In[5]:= Integrate[x^(-1), {x, 5, 6}]

Out[5]= Log[6/5]

Regards,
-- 
Jean-Marc


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