Re: Re: Trivial integral freezes 3.0
- To: mathgroup at smc.vnet.net
- Subject: [mg9892] Re: [mg9808] Re: Trivial integral freezes 3.0
- From: "W. Meeussen" <w.meeussen.vdmcc at vandemoortele.be>
- Date: Sun, 30 Nov 1997 20:16:41 -0500
- Sender: owner-wri-mathgroup at wolfram.com
hi all,
no one came up with the symbolic result sofar :
Out[56]=
27
1 + ----------------
9 + 8 Sqrt[3] Pi
I admit it is troublesome to get there, and there is a point in
regretting that Mathematica 3.0 integration routines "could not get
there from here". They need some human assistance :
step 1 : plot it (-> well behaved, no jumps) step 2 : do NIntegrate (->
1.51398, ok on sight for triangle base 4 heigth .6) step 3 : if the
definite integral gives trouble, try the indefinite one. step 4 :
"look" at the input untill a solution "occurs to you" :
In[52]:=Expand[q]
Out[52]=1/(2*(Sqrt[3]/4 + (2*Pi)/3)) - Cos[phi + Pi/3]/(Sqrt[3]/4 +
(2*Pi)/3)
In[53]:=Integrate[%, phi]
Out[53]=
(6*(phi - (-1)^(1/6)*Cos[phi] + (-1)^(5/6)*Cos[phi] -
(-1)^(1/3)*Sin[phi] +
(-1)^(2/3)*Sin[phi]))/(3*Sqrt[3] + 8*Pi)
In[54]:=(% /. phi -> 2*Pi - 2*alpha) - (% /. phi -> 0) Out[54]=
-((6*(-(-1)^(1/6) + (-1)^(5/6)))/(3*Sqrt[3] + 8*Pi)) +
(6*((1*(-1)^(1/6))/2 - (1*(-1)^(5/6))/2 + (1*(-1)^(1/3)*Sqrt[3])/2 -
(1*(-1)^(2/3)*Sqrt[3])/2 + (4*Pi)/3))/(3*Sqrt[3] + 8*Pi)
In[55]:=N[%]
Out[55]=1.513980412450272 - 2.306185360905789*^-16*I
In[56]:=FullSimplify[%%]
Out[56]=1 + 27/(9 + 8*Sqrt[3]*Pi)
In[57]:=N[%]
Out[57]=1.513980412450272
At 05:35 28-11-97 -0500, you wrote:
>On 24 Nov 1997 23:55:14 -0500, carlos at titan.Colorado.EDU (Carlos A.
>Felippa) wrote:
>
>>The following trivial Integrate statement (from a class example) appears
>>to freeze Mathematica 3.0 running under Mac OS 7.5.5.
>>
>>ClearAll[alpha,phi]; alpha=Pi/3;
>>q=(Cos[alpha]-Cos[alpha+phi])/(-alpha+Pi+Cos[alpha]*Sin[alpha]);
>>Print["q=",q//InputForm];
>>r1=Integrate[q,{phi,0,2*Pi-2*alpha}]; Print["r1=",r1//InputForm];
>>
>>Same freeze happens for other values of alpha, e.g alpha=Pi/6.
>>Mathematica 2.2 has no problems.
>>
>>I am curious as to whether the freeze happens on non-Mac versions.
>>
>>
>"q="\[InvisibleSpace](1/2 - Cos[phi + Pi/3])/(Sqrt[3]/4 + (2*Pi)/3)
>Works fine on my NT4.0 WS
>
>
Dr. Wouter L. J. MEEUSSEN
w.meeussen.vdmcc at vandemoortele.be
eu000949 at pophost.eunet.be