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Re: Trouble with an integral
*To*: mathgroup at smc.vnet.net
*Subject*: [mg57427] Re: Trouble with an integral
*From*: Bill Rowe <readnewsciv at earthlink.net>
*Date*: Fri, 27 May 2005 04:57:48 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
On 5/26/05 at 4:31 AM, astanoff at yahoo.fr (Valeri Astanoff) wrote:
>Could someone give me the right answer for this integral with
>parameter 'a' ?
>In[1]:=$Version
>Out[1]=5.0 for Microsoft Windows (November 18, 2003)
>In[2]:=Integrate[Sqrt[1+Sqrt[x]]/(2*Sqrt[2]*E^(a*x)*Sqrt[x]),{x,0,1
>},Assumptions -> a>0]
>Out[2]=(1/3)*(4 - Sqrt[2])
>In[3]:=%//N
>Out[3]=0.861929
>In[4]:=NIntegrate[Sqrt[1+Sqrt[x]]/(2*Sqrt[2]*E^(2*x)*Sqrt[x]),{x,0,
>1}]
>Out[4]=0.491465
By inspection, it is clear the function you are integrating is positive over the range 0<=x<=1 and has greater values for the case where a = 1 as compared to when a = 2. That means the value of the integral cannot be independent of the value of a, making the result returned by Integrate incorrect.
Given
In[10]:=NIntegrate[Sqrt[1 + Sqrt[x]]/(2*Sqrt[2]*E^(0*x)*Sqrt[x]), {x, 0, 1}]
Out[10]=
0.8619288125480162
It appears Integrate evaluated the integral with a = 0 rather than for a > 0.
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