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MathGroup Archive 2004

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Re: Simple question or how Mathematica getting on my nerves.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45820] Re: Simple question or how Mathematica getting on my nerves.
  • From: drbob at bigfoot.com (Bobby R. Treat)
  • Date: Mon, 26 Jan 2004 01:53:26 -0500 (EST)
  • References: <butdvt$9se$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Look at the exact integral, and it's very easy to see why there's a
precision problem. We have lots of very small numbers added and
subtracted.

Integrate[k[f], {f, a, b}]

-4334154990257095600667074069\
8442276800*a^62 + 28577904491\
31424623043019950179828854400*
   a^63 - 9283353662100362173\
9163101194122877942150*a^64 + 
  198044878124807726376881282\
5474621396099200*a^65 - 
  312070717045151568836297778\
55963731090048000*a^66 + 
  387340310887683648722783929\
328648339917670400*a^67 - 
  394365600840058303135893245\
6939228441220595200*a^68 + 
  338680851404671188697243309\
13838342803691571200*a^69 - 
  250381915145596200215462017\
827304891441576972800*a^70 + 
  161827434984555916571182806\
5143613774105966976000*a^71 - 
  925563023981112867277959440\
5918613224678294454400*a^72 + 
  473039931558964782977427838\
62876698224258680499200*
   a^73 - 2177688333573252289\
20239302287657592726091763379\
200*a^74 + 909045283860834545\
33884508749822195117455741225\
9840*a^75 - 34601817665755450\
26900679139443420020918193157\
568000*a^76 + 120671966716591\
30189052758072448567830526824\
275916800*a^77 - 387155893215\
73042689877598815772488456273\
561218566400*a^78 + 
  114676555712001164423181748\
391022307579341940824614400*
   a^79 - 3145641632377809718\
55255490378151468707222684900\
852000*a^80 + 801229057759650\
03877362022240568795148298435\
6602560000*a^81 - 18994991320\
54584969970631356532508997174\
294621018752000*a^82 + 
  420003996267261645109972073\
8999592469942473591168256000*
   a^83 - 8677355290846347191\
72009403760846539515171221378\
8096000*a^84 + 16777699743938\
20582337695931568286403768464\
0495201536000*a^85 - 
  304014520553919039629020483\
72409840843478951284909760000*
   a^86 + 5168945733371920039\
30169079913432604318092698168\
25881600*a^87 - 8254950922089\
59607675191354022588608469541\
39821102172800*a^88 + 
  123944498239281159571039966\
92940073655256368559073518080\
0*a^89 - 17509619592533370161\
62310643923280246536217145646\
89382400*a^90 + 2328865660090\
64529243262992048909195352107\
699174710016000*a^91 - 
  291783241035994616711305589\
31345217301724218251672001280\
0*a^92 + 34451271331478518046\
66265091997888300210518173038\
20646400*a^93 - 3834536450059\
51058577880835372637301499495\
174312896118400*a^94 + 
  402412278172114508045048787\
36075812501860897081002495360\
0*a^95 - 39822048360782164858\
62461958257502278829984606974\
20527000*a^96 + 3715942539232\
92778415678335309566044752088\
107066105516800*a^97 - 
  326935534064030834524451687\
30184042032610019397199306240\
0*a^98 + 27115210278092429027\
71728708771474739150129372882\
65062400*a^99 - 2119267750682\
48721611369322764507367770418\
006248986114560*a^100 + 
  156026313200792407380799958\
36940121008738568624576281600\
0*a^101 - 1081476504244708157\
04142716242320250521354588407\
602265600*a^102 + 70527736033\
38684026739498946989106557798\
0235963660108800*a^103 - 
  432402191157074080210814518\
77373689015071216096767804800*
   a^104 + 249002369215590832\
45805487238354726786087522004\
783232000*a^105 - 13453815832\
40327825459473152672682493587\
9192849925760000*a^106 + 
  681212938720647816920082148\
7468327973763960990263552000*
   a^107 - 322780848983173301\
33451557531200571759743084080\
27456000*a^108 + 142898099842\
63850232806584517033553923696\
52834160896000*a^109 - 
  589995942532105937642393072\
862370218819288480770976000*
   a^110 + 226712910441643943\
67946341648875781528448481794\
6560000*a^111 - 8088792768971\
51070484942689543818062390001\
18974504800*a^112 + 
  267240351069265250425703779\
43630567253002989159718400*
   a^113 - 815065038348906161\
89215997506889449381628549933\
82400*a^114 + 228672881964992\
54090821879530234775790415885\
21523200*a^115 - 587744795599\
67750776218432381350557188010\
1775168000*a^116 + 
  137734133918308264445279558\
711851810784023850342400*
   a^117 - 292643347489868043\
70637484932118635342126132851\
200*a^118 + 56000451871126156\
67564124346438152539301152947\
200*a^119 - 95747899032528917\
30461649385433048163460304608\
00*a^120 + 144849041819766396\
81886232436290365620587097600\
0*a^121 - 1915490061223140329\
5171957647990538143071462400*
   a^122 + 218023259001007842\
3840710626600549056934963200*
   a^123 - 209288716366732294\
067955832782414828826483200*
   a^124 + 164773338599840028\
34556522707948850015545344*
   a^125 - 102166008556448430\
2737879632189288815448000*
   a^126 + 467822546751514314\
27609751782865072348800*
   a^127 - 140656873668187305\
6653986381729134514275*
   a^128 + 208308224337937928\
09407642816305590400*a^129 + 
  433415499025709560066707406\
98442276800*b^62 - 
  285779044913142462304301995\
0179828854400*b^63 + 
  928335366210036217391631011\
94122877942150*b^64 - 
  198044878124807726376881282\
5474621396099200*b^65 + 
  312070717045151568836297778\
55963731090048000*b^66 - 
  387340310887683648722783929\
328648339917670400*b^67 + 
  394365600840058303135893245\
6939228441220595200*b^68 - 
  338680851404671188697243309\
13838342803691571200*b^69 + 
  250381915145596200215462017\
827304891441576972800*b^70 - 
  161827434984555916571182806\
5143613774105966976000*b^71 + 
  925563023981112867277959440\
5918613224678294454400*b^72 - 
  473039931558964782977427838\
62876698224258680499200*
   b^73 + 2177688333573252289\
20239302287657592726091763379\
200*b^74 - 909045283860834545\
33884508749822195117455741225\
9840*b^75 + 34601817665755450\
26900679139443420020918193157\
568000*b^76 - 120671966716591\
30189052758072448567830526824\
275916800*b^77 + 387155893215\
73042689877598815772488456273\
561218566400*b^78 - 
  114676555712001164423181748\
391022307579341940824614400*
   b^79 + 3145641632377809718\
55255490378151468707222684900\
852000*b^80 - 801229057759650\
03877362022240568795148298435\
6602560000*b^81 + 18994991320\
54584969970631356532508997174\
294621018752000*b^82 - 
  420003996267261645109972073\
8999592469942473591168256000*
   b^83 + 8677355290846347191\
72009403760846539515171221378\
8096000*b^84 - 16777699743938\
20582337695931568286403768464\
0495201536000*b^85 + 
  304014520553919039629020483\
72409840843478951284909760000*
   b^86 - 5168945733371920039\
30169079913432604318092698168\
25881600*b^87 + 8254950922089\
59607675191354022588608469541\
39821102172800*b^88 - 
  123944498239281159571039966\
92940073655256368559073518080\
0*b^89 + 17509619592533370161\
62310643923280246536217145646\
89382400*b^90 - 2328865660090\
64529243262992048909195352107\
699174710016000*b^91 + 
  291783241035994616711305589\
31345217301724218251672001280\
0*b^92 - 34451271331478518046\
66265091997888300210518173038\
20646400*b^93 + 3834536450059\
51058577880835372637301499495\
174312896118400*b^94 - 
  402412278172114508045048787\
36075812501860897081002495360\
0*b^95 + 39822048360782164858\
62461958257502278829984606974\
20527000*b^96 - 3715942539232\
92778415678335309566044752088\
107066105516800*b^97 + 
  326935534064030834524451687\
30184042032610019397199306240\
0*b^98 - 27115210278092429027\
71728708771474739150129372882\
65062400*b^99 + 2119267750682\
48721611369322764507367770418\
006248986114560*b^100 - 
  156026313200792407380799958\
36940121008738568624576281600\
0*b^101 + 1081476504244708157\
04142716242320250521354588407\
602265600*b^102 - 70527736033\
38684026739498946989106557798\
0235963660108800*b^103 + 
  432402191157074080210814518\
77373689015071216096767804800*
   b^104 - 249002369215590832\
45805487238354726786087522004\
783232000*b^105 + 13453815832\
40327825459473152672682493587\
9192849925760000*b^106 - 
  681212938720647816920082148\
7468327973763960990263552000*
   b^107 + 322780848983173301\
33451557531200571759743084080\
27456000*b^108 - 142898099842\
63850232806584517033553923696\
52834160896000*b^109 + 
  589995942532105937642393072\
862370218819288480770976000*
   b^110 - 226712910441643943\
67946341648875781528448481794\
6560000*b^111 + 8088792768971\
51070484942689543818062390001\
18974504800*b^112 - 
  267240351069265250425703779\
43630567253002989159718400*
   b^113 + 815065038348906161\
89215997506889449381628549933\
82400*b^114 - 228672881964992\
54090821879530234775790415885\
21523200*b^115 + 587744795599\
67750776218432381350557188010\
1775168000*b^116 - 
  137734133918308264445279558\
711851810784023850342400*
   b^117 + 292643347489868043\
70637484932118635342126132851\
200*b^118 - 56000451871126156\
67564124346438152539301152947\
200*b^119 + 95747899032528917\
30461649385433048163460304608\
00*b^120 - 144849041819766396\
81886232436290365620587097600\
0*b^121 + 1915490061223140329\
5171957647990538143071462400*
   b^122 - 218023259001007842\
3840710626600549056934963200*
   b^123 + 209288716366732294\
067955832782414828826483200*
   b^124 - 164773338599840028\
34556522707948850015545344*
   b^125 + 102166008556448430\
2737879632189288815448000*
   b^126 - 467822546751514314\
27609751782865072348800*
   b^127 + 140656873668187305\
6653986381729134514275*
   b^128 - 208308224337937928\
09407642816305590400*b^129

Bobby

gtsavdar at auth.gr (George) wrote in message news:<butdvt$9se$1 at smc.vnet.net>...
> Although the 2 results must be the same they aren't. WHY???????
> And not only this, but they differ by 10^21!!!!!! WHY???????? 
> 
> Please copy and paste this to Mathematica (i tried 5.0 and 4.2) to
> understand what i mean:
> 
> 
> \!\(k[f_] := 
>     2687176093959399272413585923303421161600\ *\((1 - f)\)\^67\ *
>       f\^61\[IndentingNewLine]
>   N[\[Integral]\_\(6214\/10000\)\%\(5242\/10000\)k[
>           f] \[DifferentialD]f]\[IndentingNewLine]
>   N[\[Integral]\_0.6214\%0.5242 k[f] \[DifferentialD]f]\)


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