Re: mathematica:- question ?
- To: mathgroup at smc.vnet.net
- Subject: [mg16622] Re: [mg16525] mathematica:- question ?
- From: BobHanlon at aol.com
- Date: Fri, 19 Mar 1999 12:53:49 -0500
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 3/16/99 6:53:41 PM, alex_punnoose at my-dejanews.com writes:
>How do you tell Mathematica that $a > 0$ in for example the following
>integral:
>
>Integrate[Sin[x],{x,0,a}];
>
>Similarly, it is sometimes necessary to define that $a$ is Real, or
Imaginary,
>or whatever ...
>
Alex,
The example which you gave does not require any assumptions about a
Integrate[Sin[x],{x,0,a}]
1 - Cos[a]
However, for other integrals
Integrate[x^n * Exp[-a*x], {x, 0, a}]
If[a > 0 && Re[n] > -1, a^(-1 - n)*
(Gamma[1 + n] - Gamma[1 + n, a^2]),
Integrate[x^n/E^(a*x), {x, 0, a}]]
You can either provide the appropriate assumptions
Integrate[x^n * Exp[-a*x], {x, 0, a},
Assumptions -> {a > 0, Re[n] > -1}]
a^(-1 - n)*(Gamma[1 + n] - Gamma[1 + n, a^2])
SetOptions[Integrate,
Assumptions -> {a > 0, Re[n] > -1}];
Integrate[x^n * Exp[-a*x], {x, 0, a}]
SetOptions[Integrate,Assumptions -> {}]; (* Reset *)
a^(-1 - n)*(Gamma[1 + n] - Gamma[1 + n, a^2])
or you can turn off GenerateConditions
Integrate[x^n * Exp[-a*x], {x, 0, a},
GenerateConditions -> False]
a^(-1 - n)*(Gamma[1 + n] - Gamma[1 + n, a^2])
SetOptions[Integrate, GenerateConditions -> False];
Integrate[x^n * Exp[-a*x], {x, 0, a}]
SetOptions[Integrate,
GenerateConditions -> Automatic]; (* Reset *)
a^(-1 - n)*(Gamma[1 + n] - Gamma[1 + n, a^2])
Bob Hanlon