Re: Re: integration problem
- To: mathgroup at smc.vnet.net
- Subject: [mg16318] Re: [mg16232] Re: [mg16172] integration problem
- From: "Kevin J. McCann" <kevinmccann at Home.com>
- Date: Sun, 7 Mar 1999 01:05:43 -0500
- Sender: owner-wri-mathgroup at wolfram.com
This problem gets even stranger:
Integrate[1/(2*x + Sqrt[3*x + 1]), {x, 0, 1}] = Infinity
Integrate[1/(2*x + Sqrt[3*x + 1]), {x, 1, 2}] = -Infinity
Integrate[1/(2*x + Sqrt[3*x + 1]), {x, 0, 2}]
\!\(Integrate::"idiv" :
"Integral of \!\(1\/\(\(2\\ x\) + \ at \(1 + \(3\\ x\)\)\)\) does not \
converge on \!\({0, 2}\)."\)
Looks serious.
Kevin
-----Original Message-----
From: Richard Finley <rfinley at medicine.umsmed.edu>
To: mathgroup at smc.vnet.net
Subject: [mg16318] [mg16232] Re: [mg16172] integration problem
>Michel,
>
>I can only speculate as to what is going wrong. If you rationalize the
>denominator of your function you get:
>
>1/(2 x + Sqrt[ 3 x + 1] ) == 2 x/((x-1)(4 x + 1) - Sqrt[3 x + 1]/((x -
>1)(4 x + 1) or the difference of two functions which each have a
>singularity at x = 1 so one can no longer assume the integral of the
>difference is the difference of the integrals. I suspect that Mathematica
is
>doing this transformation prior to evaluating the integral?? It doesn't
>do it in every case because I have tried other similar examples which give
>the correct answer. Another example which gives the wrong answer in a
>similar situation is:
>
>In(1) = Integrate[1/(1+Sqrt[x+1]),{x,0,1}]
>Out(1) = -2 + Log[4] + 2( Sqrt[2] - Log[1 + Sqrt[2])
>In(2) = %//N
>Out(2) = 0.451974
>In(3) = Integrate[(-1 + Sqrt[x+1])/x , {x,0,1}]
>Out(3) = Sum::div : Sum does not converge. .....
>etc, etc....
>In(4) = NIntegrate[(-1 + Sqrt[x+1])/x , {x,0,1}]
>Out[4] = 0.451974
>
>Perhaps someone from Wolfram can comment on the reasons for this and if it
>will be corrected in the next release??
>
>regards, RF
>
>>>> Michel Gosse <michel.gosse at interpc.fr> 03/02/99 12:13AM >>>
>Hello
>Mathematica 3.01 returns infinity for the calculus :
>Integrate[1/(2*x + Sqrt[3*x + 1]), {x, 0, 1}]
>but when i evaluate :
>NIntegrate[1/(2*x + Sqrt[3*x + 1]), {x, 0, 1}]
>it returns 0.449, which seems good.
>What is the problem with the integrate function ?
>Regards
>
>
>