Re: strange behaviour of Integration
- To: mathgroup at smc.vnet.net
- Subject: [mg89055] Re: strange behaviour of Integration
- From: Alois Steindl <Alois.Steindl at tuwien.ac.at>
- Date: Sat, 24 May 2008 03:57:43 -0400 (EDT)
- Organization: Inst. f. Mechanics II, TU Vienna
- References: <g11ra1$afj$1@smc.vnet.net>
Hello,
I just want to add strange results with Mathematica 6.0.1.0:
(I experienced this problem also with 6.0.2)
If I calculate
ih = Integrate[(ri - r)^2/r, {r, rim1, ri},
Assumptions -> {Element[rim1, Reals] && Element[ri, Reals] &&
rim1 > 0 && ri > rim1}]
I get the correct result
-((3 ri^2)/2) + 2 ri rim1 - rim1^2/2 + ri^2 Log[ri/rim1]
But when I divide the integrand by the constant (ri-rim1)^2:
ih2 = Integrate[(ri - r)^2/r/(ri - rim1)^2, {r, rim1, ri},
Assumptions -> {Element[rim1, Reals] && Element[ri, Reals] &&
rim1 > 0 && ri > rim1}]
Mathematica gives
(ri^2 (-3 + 2 Log[ri] - 2 Log[rim1]))/(2 (ri - rim1)^2)
Here the contribution (2 ri rim1 - rim1^2/2)/(ri-rim1)^2
is simply missing.
How can that happen?
Alois