       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,

In:= 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 ]

Out= 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]]

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 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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