       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 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 ArcCos[(Sqrt 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 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
>

```

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