Re: help with integration
- To: mathgroup at smc.vnet.net
- Subject: [mg121648] Re: help with integration
- From: Heike Gramberg <heike.gramberg at gmail.com>
- Date: Sat, 24 Sep 2011 22:31:29 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201109230743.DAA07691@smc.vnet.net>
You could try the Assumptions option in Integrate, e.g.
Integrate[
r^2*ArcCos[x/r] - x*Sqrt[r^2 - x^2], {x, Sqrt[3] y,
Sqrt[r^2 - y^2]},
Assumptions -> (r >= 0 && y > 0 && r > 2 y)]
which gives
y^3/3 + 2/3 r^2 Sqrt[r^2 - 3 y^2] + y^2 Sqrt[r^2 - 3 y^2] -
r^2 y (1 + Sqrt[3] ArcCos[(Sqrt[3] y)/r]) +
r^2 Sqrt[(r - y) (r + y)] ArcSec[r/Sqrt[r^2 - y^2]]
The extra advantage is that using Assumptions might help to speed up the
integration as well.
Heike.
On 23 Sep 2011, at 09:43, Salman Durrani wrote:
> I am trying to do the following integration:
>
> Integrate[r^2*ArcCos[x/r] - x*Sqrt[r^2 - x^2], {x, Sqrt[3] y, Sqrt[r^2
- y^2]} ]
>
> When I try, Mathematica comes back to be with a very long conditional
expression.
>
> How do I tell mathematica that r is positive, real in the above
equation not complex.
>
> Thanks
>
> Kahless
>
- References:
- help with integration
- From: Salman Durrani <dsalman96@yahoo.com>
- help with integration