Re: Error?

*To*: mathgroup at smc.vnet.net*Subject*: [mg44721] Re: Error?*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Sat, 22 Nov 2003 02:17:15 -0500 (EST)*References*: <bpkoo5$cbi$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"Baris Altunkaynak" <altunkai at boun.edu.tr> wrote: > This integral below give 0 on Mathematica 5.0 > Integrate[Sqrt[R^2 - x^2], {x, -R, -R + d}, > Assumptions -> R > 0 && d > 0 && d < 2R] > > This is a mistake I think, isn't it? Certainly! (And please report this bug!) Here's my best suggestion for getting a correct answer from Mathematica: In[1]:= Integrate[Sqrt[R^2 - x^2], x] Out[1]= (1/2)*(x*Sqrt[R^2 - x^2] + R^2*ArcTan[x/Sqrt[R^2 - x^2]]) In[2]:= Limit[%, x -> -R] Out[2]= -((Pi*R^2)/4) In[3]:= Simplify[%% /. x -> -R + d] Out[3]= (1/2)*(Sqrt[(-d)*(d - 2*R)]*(d - R) + R^2*ArcTan[(d - R)/Sqrt[(-d)*(d - 2*R)]]) In[4]:= % - %% Out[4]= (Pi*R^2)/4 + (1/2)*(Sqrt[(-d)*(d - 2*R)]*(d - R) + R^2*ArcTan[(d - R)/Sqrt[(-d)*(d - 2*R)]]) I believe that is correct. Unfortunately though, I am unable to get FullSimplify to give me the simpler result (1/2)*(Sqrt[d*(2*R - d)]*(d - R) + R^2*ArcCos[1 - d/R]) But that may just be due to lack of cleverness on my part. David Cantrell

**Follow-Ups**:**Re: Re: Error?***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>