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. -- To reply via email subtract one hundred and four