Re: Integrate bug
- To: mathgroup at smc.vnet.net
- Subject: [mg108247] Re: [mg108232] Integrate bug
- From: Leonid Shifrin <lshifr at gmail.com>
- Date: Thu, 11 Mar 2010 07:21:26 -0500 (EST)
- References: <201003111136.GAA06024@smc.vnet.net>
Hi Daniel,
Indeed, looks like a bug. Interestingly, indefinite integration is correct:
In[1]:= Integrate[1/(6 (4 - Y)^(1/3)), Y]
Out[1]= -(1/4) (4 - Y)^(2/3)
In[2]:=
Subtract @@ (# /. {{Y -> 4}, {Y -> -4}}) &@
Integrate[1/(6 (4 - Y)^(1/3)), Y]
Out[2]= 1
Regards,
Leonid
On Thu, Mar 11, 2010 at 2:36 PM, Daniel <daniel.ernesto.acuna at gmail.com>wrote:
> Hello,
>
> I was working with the following probability distribution
>
> P(Y) = 1/(6 (4 - Y)^(1/3)), for -4 < Y < 4
>
> and I tried to check whether it would sum up to 1. But it didn't work
> with Integrate:
>
> Integrate[1/(6 (4 - Y)^(1/3)), {Y, -4, 4}] = 0
>
> Clearly, the integral is 1. It is surprising that NIntegrate gives the
> right answer:
>
> NIntegrate[1/(6 (4 - Y)^(1/3)), {Y, -4, 4}] = 1.
>
> Wolfram Alpha seems to have the bug as well:
>
>
> http://www.wolframalpha.com/input/?i=integrate+1%2F%286+%284+-+Y%29%5E%281%2F3%29%29+from+-4+to+4
>
> Cheers,
> Daniel
>
- References:
- Integrate bug
- From: Daniel <daniel.ernesto.acuna@gmail.com>
- Integrate bug