Valeur approchée d'une intégrale: méthode des rectangles
Author: H. Abderrahim

Il s'agit d'une illustration graphique de:
* la méthode des rectangles pour encadrer une intégrale
* la notion de deux suites adjacentes(ordonnées des ponts E et F)
Le curseur n commande le nombre de subdivisions

≤

H. Abderrahim

O = (0, 0)
Q = (6, 0)
a' = Segment(O, Q)
f(x) = 0.5 * x * sqrt(36 - 6 * x)
A1 = 0.36
B1 = 1.0470988492019302
A2 = 0.34
B2 = 0.9906785553346751
A3 = 0.36
B3 = 1.0470988492019302
A4 = 0.38
B4 = 1.1033095667128094
A5 = 0.4
B5 = 1.1593101396951546
A6 = 0.42
B6 = 1.2150999958851116
A7 = 0.5
B7 = 1.4361406616345072
A8 = 0.52
B8 = 1.4908682034304697
A9 = 0.54
B9 = 1.5453815062954561
A10 = 0.56
B10 = 1.5996799679935982
A11 = 0.58
B11 = 1.653762981808459
A12 = 0.6
B12 = 1.7076299364909282
A13 = 0.62
B13 = 1.76128021620638
A14 = 0.66
B14 = 1.8679282641472028
A15 = 0.72
B15 = 2.02625960824372
A16 = 0.74
B16 = 2.078596641967845
A17 = 0.76
B17 = 2.130712556869181
A18 = 0.8
B18 = 2.234278407003025
A19 = 0.8200000000000001
B19 = 2.2857270178216815
A20 = 0.84
B20 = 2.3369518608649145
A21 = 0.86
B21 = 2.3879522608293478
A22 = 1
B22 = 2.7386127875258275
A23 = 1.1400000000000001
B23 = 3.077999999999996
A24 = 1.16
B24 = 3.1255489117913413
A25 = 1.18
B25 = 3.1728617997007085
A26 = 1.26
B26 = 3.3597374897452923
A27 = 1.3
B27 = 3.451738692311455
A28 = 1.32
B28 = 3.497377303065832
A29 = 1.34
B29 = 3.542773489795813
A30 = 1.36
B30 = 3.5879264206502306
A31 = 1.3800000000000001
B31 = 3.6328352563803357
A32 = 1.42
B32 = 3.721917247871044
A33 = 1.48
B33 = 3.8536881036222965
A34 = 1.5
B34 = 3.897114317029974
A35 = 1.52
B35 = 3.9402903446319755
A36 = 1.54
B36 = 3.9832152841642916
A37 = 1.58
B37 = 4.068308247908451
A38 = 1.6600000000000001
B38 = 4.235440472961457
A39 = 1.7
B39 = 4.317464533728099
A40 = 1.76
B40 = 4.4385511149473125
A41 = 1.78
B41 = 4.47838944264565
A42 = 1.82
B42 = 4.5572741852998035
A43 = 1.84
B43 = 4.596318526821221
A44 = 2
B44 = 4.898979485566354
A45 = 2.14
B45 = 5.149357629840829
A46 = 2.16
B46 = 5.184000000000001
A47 = 2.18
B47 = 5.218357212763415
A48 = 2.24
B48 = 5.319705254992986
A49 = 2.2600000000000002
B49 = 5.352909115611801
A50 = 2.3000000000000003
B50 = 5.41844073511928
A51 = 2.36
B51 = 5.514527722298617
A52 = 2.4
B52 = 5.577096018538683
A53 = 2.42
B53 = 5.607929029508128
A54 = 2.44
B54 = 5.63845936404617
A55 = 2.46
B55 = 5.668685561927035
A56 = 2.48
B56 = 5.698606145365723
A57 = 2.5
B57 = 5.728219618694794
A58 = 2.52
B58 = 5.757524468033111
A59 = 2.58
B59 = 5.843571852899554
A60 = 2.6
B60 = 5.871626691130835
A61 = 2.64
B61 = 5.926785300649929
A62 = 2.66
B62 = 5.953885789969441
A63 = 2.68
B63 = 5.980664845984933
A64 = 2.7
B64 = 6.007120774547481
A65 = 2.74
B65 = 6.059056362173898
A66 = 2.7600000000000002
B66 = 6.084532521073413
A67 = 2.7800000000000002
B67 = 6.109678551282386
A68 = 2.8000000000000003
B68 = 6.1344926440578575
A69 = 2.84
B69 = 6.183117660209934
A70 = 2.86
B70 = 6.206924842464261
A71 = 3
B71 = 6.363961030678926
A72 = 3.22
B72 = 6.575426069845207
A73 = 3.3200000000000003
B73 = 6.656579301713453
A74 = 3.34
B74 = 6.6716447747163485
A75 = 3.36
B75 = 6.686315577356481
A76 = 3.4
B76 = 6.714462003764709
A77 = 3.46
B77 = 6.753650568396324
A78 = 3.56
B78 = 6.8106810232164
A79 = 3.6
B79 = 6.830519745963695
A80 = 3.62
B80 = 6.83978859322421
A81 = 3.64
B81 = 6.848619130890544
A82 = 3.66
B82 = 6.857007802241437
A83 = 3.68
B83 = 6.864950983073365
A84 = 3.74
B84 = 6.886070287181212
A85 = 3.7600000000000002
B85 = 6.892193845213589
A86 = 3.8200000000000003
B86 = 6.907759984249603
A87 = 4
B87 = 6.928203230275505
A88 = 4.14
B88 = 6.915163338634885
A89 = 4.18
B89 = 6.906493466296775
A90 = 4.22
B90 = 6.8955368173913705
A91 = 4.24
B91 = 6.889184567131295
A92 = 4.28
B92 = 6.874697957001461
A93 = 4.32
B93 = 6.857787398279418
A94 = 4.34
B94 = 6.848404485717822
A95 = 4.4
B95 = 6.816450689325061
A96 = 4.42
B96 = 6.804503508706565
A97 = 4.44
B97 = 6.791893992105596
A98 = 4.46
B98 = 6.778613132492513
A99 = 4.48
B99 = 6.764651654002588
A100 = 4.5
B100 = 6.7500000000000036
A101 = 4.5200000000000005
B101 = 6.7346483204396
A102 = 4.54
B102 = 6.718586458474729
A103 = 4.5600000000000005
B103 = 6.701803936254782
A104 = 4.58
B104 = 6.684289939851505
A105 = 4.6000000000000005
B105 = 6.6660333032471435
A106 = 4.66
B106 = 6.606690245501152
A107 = 4.68
B107 = 6.585343726792097
A108 = 4.7
B108 = 6.563192820571402
A109 = 4.72
B109 = 6.540223849380082
A110 = 4.76
B110 = 6.491774487765268
A111 = 4.78
B111 = 6.466264145548024
A112 = 4.8
B112 = 6.439875775199393
A113 = 4.82
B113 = 6.41259292330334
A114 = 4.84
B114 = 6.384398483804086
A115 = 4.86
B115 = 6.355274659682301
A116 = 4.88
B116 = 6.325202921646067
A117 = 4.9
B117 = 6.294163963545913
A118 = 4.92
B118 = 6.262137654188059
A119 = 4.94
B119 = 6.229102985181742
A120 = 4.98
B120 = 6.159919804672786
A121 = 5
B121 = 6.123724356957947
A122 = 5.0200000000000005
B122 = 6.08642653779704
A123 = 5.04
B123 = 6.047999999999995
A124 = 5.0600000000000005
B124 = 6.008417096041196
A125 = 5.08
B125 = 5.967648783231125
A126 = 5.1000000000000005
B126 = 5.925664519697349
A127 = 5.14
B127 = 5.8379177794826855
A128 = 5.16
B128 = 5.79208563472606
A129 = 5.18
B129 = 5.744897910320068
A130 = 5.2
B130 = 5.6963145980537355
A131 = 5.22
B131 = 5.646293297376612
A132 = 5.24
B132 = 5.5947890040644115
A133 = 5.26
B133 = 5.54175387400055
A134 = 5.3
B134 = 5.430883905958581
A135 = 5.32
B135 = 5.3729366272086345
A136 = 5.34
B136 = 5.313232914149356
A137 = 5.36
B137 = 5.251706008527137
A138 = 5.38
B138 = 5.188284109414209
A139 = 5.4
B139 = 5.12288980947277
A140 = 5.42
B140 = 5.05543944677413
A141 = 5.44
B141 = 4.985842356111956
A142 = 5.48
B142 = 4.83980495474767
A143 = 5.5
B143 = 4.763139720814415
A144 = 5.5200000000000005
B144 = 4.683875318579684
A145 = 5.54
B145 = 4.601869620056609
A146 = 5.5600000000000005
B146 = 4.516965352977605
A147 = 5.5200000000000005
B147 = 4.683875318579684
A148 = 5.42
B148 = 5.05543944677413
A149 = 5.28
B149 = 5.4871369583781995
A150 = 5.22
B150 = 5.646293297376612
A151 = 5.18
B151 = 5.744897910320068
A152 = 5.14
B152 = 5.8379177794826855
A153 = 5
B153 = 6.123724356957947
A154 = 4.84
B154 = 6.384398483804086
A155 = 4.78
B155 = 6.466264145548024
A156 = 4.72
B156 = 6.540223849380082
A157 = 4.48
B157 = 6.764651654002588
A158 = 4.34
B158 = 6.848404485717822
A159 = 4.2
B159 = 6.901304224565095
A160 = 4
B160 = 6.928203230275505
f' = Derivative(f)
a = Integral(f', 0, 4)
n = 48 (slider from 0 to 50, step 1)
d = LowerSum(f', 0, 4, n)
e = UpperSum(f', 0, 4, n)
text1: "≤ i = " + a
b: y = a
E: (n, d)
F: (n, e)
texte2: "s_i =" + d + ""
texte1: "s_s=" + e + ""