Re: Re: Integrate bug
- To: mathgroup at smc.vnet.net
- Subject: [mg108273] Re: [mg108247] Re: [mg108232] Integrate bug
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Fri, 12 Mar 2010 07:10:58 -0500 (EST)
- References: <201003111136.GAA06024@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
This also works:
p[y_] = 1/(6 (4 - y)^(1/3));
Integrate[p@y, {y, -4, 0}]
Integrate[p@y, {y, 0, 4}]
%% + %
1 - 1/2^(2/3)
1/2^(2/3)
1
and
q[y_] = Integrate[p@y, y]
q[4] - q[-4]
-(1/4) (4 - y)^(2/3)
1
Bobby
On Thu, 11 Mar 2010 06:21:26 -0600, Leonid Shifrin <lshifr at gmail.com>
wrote:
> 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
>>
--
DrMajorBob at yahoo.com
- References:
- Integrate bug
- From: Daniel <daniel.ernesto.acuna@gmail.com>
- Integrate bug