Re: Integrate with If
- To: mathgroup at smc.vnet.net
- Subject: [mg22203] Re: [mg22180] Integrate with If
- From: schadow at netcom.ca
- Date: Fri, 18 Feb 2000 02:34:39 -0500 (EST)
- References: <200002170624.BAA04409@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
> Why does
>
> Integrate[If[Sin[t] > 0, 1, 0] , {t, -Pi, Pi}]
>
> evaluate to 2Pi?
>
> Plot[If[Sin[t] > 0, 1, 0] , {t, -Pi, Pi} ]
>
> looks all right.
>
>
> Puzzled,
>
> Johan Berglind,
> Chalmers, Goteborg,
> Sweden.
>
I have no an answer, but here are some other 'interesting' results
f[x_] = If[Sin[x] > 0, 1, 0]
Integrate[f[x], {x, -\[Pi], 0}]
gives 0 (correc)
Integrate[f[x], {x, -\[Pi], 2}]
gives 0 (wrong)
\!\(Integrate[f[x], {x, \(-\[Pi]\), \[Pi] - 1\/100000}]\)
gives 0 (wrong).
One way to get a correct result is:
Integrate[f[x], {x, -\[Pi], 0, \[Pi]}]
or with NIntegrate
NIntegrate[f[x], {x, -\[Pi], 0, \[Pi]}]
NIntegrate[f[x], {x, -\[Pi], \[Pi]}]
Wolfgang
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- References:
- Integrate with If
- From: "Johan Berglind,5879" <johanbe@chl.chalmers.se>
- Integrate with If