[Date Index]
[Thread Index]
[Author Index]
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
Prev by Date:
**Re: Mesh generation in 2D**
Next by Date:
**RE: Error?**
Previous by thread:
**Error?**
Next by thread:
**Re: Re: Error?**
| |