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>