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Re: help with integration

  • To: mathgroup at
  • Subject: [mg121654] Re: help with integration
  • From: Richard Hofler <rhofler at>
  • Date: Sat, 24 Sep 2011 22:32:35 -0400 (EDT)
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  • References: <>


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]]


-----Original Message-----
From: Salman Durrani [mailto:dsalman96 at]
Sent: Friday, September 23, 2011 3:43 AM
To: mathgroup at
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.



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