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