Re: help with integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg121654] Re: help with integration*From*: Richard Hofler <rhofler at bus.ucf.edu>*Date*: Sat, 24 Sep 2011 22:32:35 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201109230743.DAA07691@smc.vnet.net>

Hello, You should read about the Assumptions option for Integrate. In[6]:= 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 ] Out[6]= 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]] Richard -----Original Message----- From: Salman Durrani [mailto:dsalman96 at yahoo.com] Sent: Friday, September 23, 2011 3:43 AM To: mathgroup at smc.vnet.net Subject: [mg121654] help with integration 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>