Comparison Approximation
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ABCDEFG
1
Number of Iterations
Composite Trapazoid x^3
Composite Midpoint x^3
Composite Simpson x^3
Composite Trapazoid sin(x)
Composite Midpoint sin(x)
Composite Simpson sin(x)
2
1078.125208.333333301.1107207350.523598776
3
239.0625136.71875156.250.5553603671.0261721531.002279877
4
369.44444444147.569444479.732510290.7152492291.011515160.523598776
5
487.890625151.3671875156.250.790766261.0064545431.000134585
6
5100153.12584.333333330.8346821361.0041242040.696146193
7
6108.5069444154.0798611156.250.8633821941.0028615081.000026312
8
7114.7959184154.655612295.35957240.8836004761.0021012160.779365472
9
8119.6289063155.0292969156.250.8986104011.0016081891.000008296
10
9123.4567901155.2854938104.43656960.9101937691.0012703680.827239947
11
10126.5625155.46875156.250.919403171.0010288241.000003392
12
11129.1322314155.6043388111.43079940.9269002771.0008501620.858171646
13
12131.2934028155.7074653156.250.9331218511.0007143041.000001634
14
13133.1360947155.7877219116.86244650.9383677931.0006085930.879758026
15
14134.7257653155.8514031156.250.9428508461.0005247251.000000882
16
15136.1111111155.9027778121.16460910.9467261031.0004570720.895663358
17
16137.3291016155.9448242156.250.9501092951.0004017081.000000517
18
17138.4083045155.9796713124.64180670.953088531.0003558270.907863396
19
18139.371142156.0088735156.250.9557320691.000317381.000000322
20
19140.2354571156.0335873127.50407330.9580936141.0002848450.917515017
21
20141.015625156.0546875156.250.9602159971.0002570671.000000212
22
21141.723356156.0728458129.89807920.9621337931.0002331640.925339786
23
22142.3682851156.0885847156.250.9638752191.0002124461.000000144
24
23142.9584121156.1023157131.92833910.9654635341.0001943710.93181077
25
24143.500434156.1143663156.250.9669180771.0001785091.000000102
26
25144156.125133.67093330.9682550651.0001645120.93725089
27
26144.4619083156.1344305156.250.9694881931.00015211.000000074
28
27144.8902606156.1428326135.18237840.970629111.0001410410.94188804
29
28145.2885842156.1503508156.250.9716877861.0001311451.000000055
30
29145.6599287156.1571046136.5054460.9726728021.0001222560.945887616
31
30146.0069444156.1631944156.250.9735915881.0001142411.000000042
32
31146.3319459156.1687045137.6730560.9744506051.0001069890.949372544
33
32146.6369629156.1737061156.250.9752555021.0001004061.000000032
34
33146.9237833156.1782599138.7109330.9760112361.0000944120.952436083
35
34147.1939879156.1824178156.250.9767221791.000088941.000000025
36
35147.4489796156.1862245139.63945580.9773921961.000083930.955150255
37
36147.6900077156.1897184156.250.9780247241.0000793321.00000002
38
37147.9181885156.1929328140.4749690.9786228231.0000751010.957571565
39
38148.1345222156.1958968156.250.9791892291.00007121.000000016
40
39148.339908156.1986358141.23072870.9797263971.0000675960.959744962
41
40148.5351563156.2011719156.250.9802365321.0000642581.000000013
42
41148.7209994156.2035247141.91759610.9807216261.0000611620.961706649
43
42148.8981009156.2057115156.250.9811834781.0000582841.000000011
44
43149.0670633156.2077474142.54455240.981623721.0000556040.96348611
45
44149.2284349156.2096462156.250.9820438321.0000531051.000000009
46
45149.382716156.2114198143.11908750.9824451661.0000507710.965107599
47
46149.5303639156.2130789156.250.9828289531.0000485881.000000008
48
47149.6717972156.2146333143.64749630.9831963181.0000465420.966591251
49
48149.8074002156.2160916156.250.9835482931.0000446231.000000006
50
49149.937526156.2174615144.13510690.9838858271.000042820.967953918
51
50150.0625156.21875156.250.9842097891.0000411251.000000005
52
51150.1826221156.2199635144.58645920.9845209821.0000395280.969209816
53
52150.2981694156.2211076156.250.9848201461.0000380221.000000005
54
53150.4093984156.2221876145.0054450.9851079661.0000366010.970371015
55
54150.5165466156.2232082156.250.9853850751.0000352581.000000004
56
55150.6198347156.2241736145.39541930.985652061.0000339870.971447835
57
56150.7194675156.2250877156.250.9859094651.0000327841.000000003
58
57150.8156356156.2259541145.75928970.9861577981.0000316440.972449149
59
58150.9085166156.2267762156.250.9863975291.0000305621.000000003
60
59150.9982764156.2275567146.09958870.9866290981.0000295350.973382626
61
60151.0850694156.2282986156.250.9868529141.0000285581.000000003
62
61151.1690406156.2290043146.41853160.9870693611.000027630.974254934
63
62151.2503252156.2296761156.250.9872787971.0000267461.000000002
64
63151.3290501156.2303162146.71806520.9874815561.0000259030.975071894
65
64151.4053345156.2309265156.250.9876779541.00002511.000000002
66
65151.4792899156.2315089146.99990660.9878682841.0000243340.975838609
67
66151.5510216156.232065156.250.9880528241.0000236021.000000002
68
67151.6206282156.2325963147.26557690.9882318341.0000229030.976559576
69
68151.6882029156.2331045156.250.9884055591.0000222341.000000002
70
69151.7538332156.2335906147.51642740.988574231.0000215940.97723877
71
70151.817602156.2340561156.250.9887380631.0000209821.000000001
72
71151.8795874156.2345021147.75366330.9888972651.0000203950.977879719
73
72151.939863156.2349296156.250.9890520281.0000198321.000000001
74
73151.9984988156.2353397147.97836280.9892025361.0000192930.978485564
75
74152.0555606156.2357332156.250.9893489621.0000187751.000000001
76
75152.1111111156.2361111148.1914930.989491471.0000182770.979059112
77
76152.1652095156.2364742156.250.9896302151.0000177991.000000001
78
77152.217912156.2368232148.39392440.9897653441.000017340.979602878
79
78152.2692719156.2371589156.250.9898969961.0000168981.000000001
80
79152.3193398156.237482148.58644220.9900253051.0000164730.980119123
81
80152.3681641156.237793156.250.9901503951.0000160641.000000001
82
81152.4157903156.2380925148.76975670.9902723871.000015670.980609884
83
82152.462262156.2383812156.250.9903913941.000015291.000000001
84
83152.5076208156.2386595148.94451190.9905075241.0000149240.981077003
85
84152.5519062156.2389279156.250.9906208811.000014571.000000001
86
85152.5951557156.2391869149.11129340.9907315621.000014230.981522147
87
86152.6374054156.2394369156.250.9908396621.0000139011.000000001
88
87152.6786894156.2396783149.27063420.9909452691.0000135830.981946832
89
88152.7190405156.2399115156.250.9910484691.0000132761.000000001
90
89152.7584901156.240137149.42302120.9911493431.0000129790.982352436
91
90152.7970679156.2403549156.250.9912479691.0000126931.000000001
92
91152.8348026156.2405658149.56889960.9913444211.0000124150.982740217
93
92152.8717214156.2407697156.250.991438771.0000121471
94
93152.9078506156.2409672149.70867750.9915310851.0000118870.983111323
95
94152.9432153156.2411583156.250.991621431.0000116351
96
95152.9778393156.2413435149.84272940.9917098681.0000113920.983466809
97
96153.0117459156.2415229156.250.9917964581.0000111561
98
97153.044957156.2416968149.97140.9918812581.0000109270.983807639
99
98153.0774938156.2418654156.250.9919643231.0000107051
100
99153.1093766156.2420289150.09500670.9920457061.000010490.984134702
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