Sample spreadsheet showing numerical integration for the area
under the standard normal curve from x=0 to x=1:
dx: 0.001 area under the
x y normal curve from x=0 to x=1
0.0005 0.39894 sum= 341.3448
0.0015 0.39894 area= 0.341345
0.0025 0.39894 numerical integration
0.0035 0.39894 with 1000 rectangles
0.0045 0.39894
0.0055 0.39894 y=e^(x^2/2)/sqrt(2*pi)
0.0065 0.39893
0.0075 0.39893
0.0085 0.39893
0.0095 0.39892
0.0105 0.39892
0.0115 0.39892
0.0125 0.39891
0.0135 0.39891
0.0145 0.39890
0.0155 0.39889
0.0165 0.39889
0.0175 0.39888
0.0185 0.39887
0.0195 0.39887
0.0205 0.39886
0.0215 0.39885
0.0225 0.39884
0.0235 0.39883
0.0245 0.39882
0.0255 0.39881
0.0265 0.39880
0.0275 0.39879
0.0285 0.39878
0.0295 0.39877
0.0305 0.39876
0.0315 0.39874
0.0325 0.39873
0.0335 0.39872
0.0345 0.39870
0.0355 0.39869
0.0365 0.39868
0.0375 0.39866
0.0385 0.39865
0.0395 0.39863
0.0405 0.39862
0.0415 0.39860
0.0425 0.39858
0.0435 0.39857
0.0445 0.39855
0.0455 0.39853
0.0465 0.39851
0.0475 0.39849
0.0485 0.39847
0.0495 0.39845
0.0505 0.39843
0.0515 0.39841
0.0525 0.39839
0.0535 0.39837
0.0545 0.39835
0.0555 0.39833
0.0565 0.39831
0.0575 0.39828
0.0585 0.39826
0.0595 0.39824
0.0605 0.39821
0.0615 0.39819
0.0625 0.39816
0.0635 0.39814
0.0645 0.39811
0.0655 0.39809
0.0665 0.39806
0.0675 0.39803
0.0685 0.39801
0.0695 0.39798
0.0705 0.39795
0.0715 0.39792
0.0725 0.39790
0.0735 0.39787
0.0745 0.39784
0.0755 0.39781
0.0765 0.39778
0.0775 0.39775
0.0785 0.39771
0.0795 0.39768
0.0805 0.39765
0.0815 0.39762
0.0825 0.39759
0.0835 0.39755
0.0845 0.39752
0.0855 0.39749
0.0865 0.39745
0.0875 0.39742
0.0885 0.39738
0.0895 0.39735
0.0905 0.39731
0.0915 0.39728
0.0925 0.39724
0.0935 0.39720
0.0945 0.39716
0.0955 0.39713
0.0965 0.39709
0.0975 0.39705
0.0985 0.39701
0.0995 0.39697
0.1005 0.39693
0.1015 0.39689
0.1025 0.39685
0.1035 0.39681
0.1045 0.39677
0.1055 0.39673
0.1065 0.39669
0.1075 0.39664
0.1085 0.39660
0.1095 0.39656
0.1105 0.39651
0.1115 0.39647
0.1125 0.39643
0.1135 0.39638
0.1145 0.39634
0.1155 0.39629
0.1165 0.39624
0.1175 0.39620
0.1185 0.39615
0.1195 0.39610
0.1205 0.39606
0.1215 0.39601
0.1225 0.39596
0.1235 0.39591
0.1245 0.39586
0.1255 0.39581
0.1265 0.39576
0.1275 0.39571
0.1285 0.39566
0.1295 0.39561
0.1305 0.39556
0.1315 0.39551
0.1325 0.39546
0.1335 0.39540
0.1345 0.39535
0.1355 0.39530
0.1365 0.39524
0.1375 0.39519
0.1385 0.39513
0.1395 0.39508
0.1405 0.39502
0.1415 0.39497
0.1425 0.39491
0.1435 0.39486
0.1445 0.39480
0.1455 0.39474
0.1465 0.39468
0.1475 0.39463
0.1485 0.39457
0.1495 0.39451
0.1505 0.39445
0.1515 0.39439
0.1525 0.39433
0.1535 0.39427
0.1545 0.39421
0.1555 0.39415
0.1565 0.39409
0.1575 0.39402
0.1585 0.39396
0.1595 0.39390
0.1605 0.39384
0.1615 0.39377
0.1625 0.39371
0.1635 0.39365
0.1645 0.39358
0.1655 0.39352
0.1665 0.39345
0.1675 0.39338
0.1685 0.39332
0.1695 0.39325
0.1705 0.39319
0.1715 0.39312
0.1725 0.39305
0.1735 0.39298
0.1745 0.39291
0.1755 0.39285
0.1765 0.39278
0.1775 0.39271
0.1785 0.39264
0.1795 0.39257
0.1805 0.39250
0.1815 0.39243
0.1825 0.39235
0.1835 0.39228
0.1845 0.39221
0.1855 0.39214
0.1865 0.39206
0.1875 0.39199
0.1885 0.39192
0.1895 0.39184
0.1905 0.39177
0.1915 0.39169
0.1925 0.39162
0.1935 0.39154
0.1945 0.39147
0.1955 0.39139
0.1965 0.39131
0.1975 0.39124
0.1985 0.39116
0.1995 0.39108
0.2005 0.39100
0.2015 0.39092
0.2025 0.39085
0.2035 0.39077
0.2045 0.39069
0.2055 0.39061
0.2065 0.39053
0.2075 0.39045
0.2085 0.39036
0.2095 0.39028
0.2105 0.39020
0.2115 0.39012
0.2125 0.39004
0.2135 0.38995
0.2145 0.38987
0.2155 0.38979
0.2165 0.38970
0.2175 0.38962
0.2185 0.38953
0.2195 0.38945
0.2205 0.38936
0.2215 0.38927
0.2225 0.38919
0.2235 0.38910
0.2245 0.38901
0.2255 0.38893
0.2265 0.38884
0.2275 0.38875
0.2285 0.38866
0.2295 0.38857
0.2305 0.38848
0.2315 0.38839
0.2325 0.38830
0.2335 0.38821
0.2345 0.38812
0.2355 0.38803
0.2365 0.38794
0.2375 0.38785
0.2385 0.38776
0.2395 0.38766
0.2405 0.38757
0.2415 0.38748
0.2425 0.38738
0.2435 0.38729
0.2445 0.38719
0.2455 0.38710
0.2465 0.38700
0.2475 0.38691
0.2485 0.38681
0.2495 0.38672
0.2505 0.38662
0.2515 0.38652
0.2525 0.38643
0.2535 0.38633
0.2545 0.38623
0.2555 0.38613
0.2565 0.38603
0.2575 0.38593
0.2585 0.38583
0.2595 0.38573
0.2605 0.38563
0.2615 0.38553
0.2625 0.38543
0.2635 0.38533
0.2645 0.38523
0.2655 0.38513
0.2665 0.38502
0.2675 0.38492
0.2685 0.38482
0.2695 0.38471
0.2705 0.38461
0.2715 0.38451
0.2725 0.38440
0.2735 0.38430
0.2745 0.38419
0.2755 0.38409
0.2765 0.38398
0.2775 0.38387
0.2785 0.38377
0.2795 0.38366
0.2805 0.38355
0.2815 0.38344
0.2825 0.38334
0.2835 0.38323
0.2845 0.38312
0.2855 0.38301
0.2865 0.38290
0.2875 0.38279
0.2885 0.38268
0.2895 0.38257
0.2905 0.38246
0.2915 0.38235
0.2925 0.38224
0.2935 0.38212
0.2945 0.38201
0.2955 0.38190
0.2965 0.38179
0.2975 0.38167
0.2985 0.38156
0.2995 0.38144
0.3005 0.38133
0.3015 0.38122
0.3025 0.38110
0.3035 0.38099
0.3045 0.38087
0.3055 0.38075
0.3065 0.38064
0.3075 0.38052
0.3085 0.38040
0.3095 0.38029
0.3105 0.38017
0.3115 0.38005
0.3125 0.37993
0.3135 0.37981
0.3145 0.37969
0.3155 0.37957
0.3165 0.37945
0.3175 0.37933
0.3185 0.37921
0.3195 0.37909
0.3205 0.37897
0.3215 0.37885
0.3225 0.37873
0.3235 0.37860
0.3245 0.37848
0.3255 0.37836
0.3265 0.37823
0.3275 0.37811
0.3285 0.37799
0.3295 0.37786
0.3305 0.37774
0.3315 0.37761
0.3325 0.37749
0.3335 0.37736
0.3345 0.37724
0.3355 0.37711
0.3365 0.37698
0.3375 0.37686
0.3385 0.37673
0.3395 0.37660
0.3405 0.37647
0.3415 0.37634
0.3425 0.37622
0.3435 0.37609
0.3445 0.37596
0.3455 0.37583
0.3465 0.37570
0.3475 0.37557
0.3485 0.37544
0.3495 0.37531
0.3505 0.37517
0.3515 0.37504
0.3525 0.37491
0.3535 0.37478
0.3545 0.37465
0.3555 0.37451
0.3565 0.37438
0.3575 0.37425
0.3585 0.37411
0.3595 0.37398
0.3605 0.37384
0.3615 0.37371
0.3625 0.37357
0.3635 0.37344
0.3645 0.37330
0.3655 0.37317
0.3665 0.37303
0.3675 0.37289
0.3685 0.37275
0.3695 0.37262
0.3705 0.37248
0.3715 0.37234
0.3725 0.37220
0.3735 0.37206
0.3745 0.37192
0.3755 0.37179
0.3765 0.37165
0.3775 0.37151
0.3785 0.37137
0.3795 0.37122
0.3805 0.37108
0.3815 0.37094
0.3825 0.37080
0.3835 0.37066
0.3845 0.37052
0.3855 0.37037
0.3865 0.37023
0.3875 0.37009
0.3885 0.36994
0.3895 0.36980
0.3905 0.36966
0.3915 0.36951
0.3925 0.36937
0.3935 0.36922
0.3945 0.36908
0.3955 0.36893
0.3965 0.36878
0.3975 0.36864
0.3985 0.36849
0.3995 0.36834
0.4005 0.36820
0.4015 0.36805
0.4025 0.36790
0.4035 0.36775
0.4045 0.36760
0.4055 0.36746
0.4065 0.36731
0.4075 0.36716
0.4085 0.36701
0.4095 0.36686
0.4105 0.36671
0.4115 0.36656
0.4125 0.36640
0.4135 0.36625
0.4145 0.36610
0.4155 0.36595
0.4165 0.36580
0.4175 0.36565
0.4185 0.36549
0.4195 0.36534
0.4205 0.36519
0.4215 0.36503
0.4225 0.36488
0.4235 0.36472
0.4245 0.36457
0.4255 0.36441
0.4265 0.36426
0.4275 0.36410
0.4285 0.36395
0.4295 0.36379
0.4305 0.36364
0.4315 0.36348
0.4325 0.36332
0.4335 0.36316
0.4345 0.36301
0.4355 0.36285
0.4365 0.36269
0.4375 0.36253
0.4385 0.36237
0.4395 0.36221
0.4405 0.36206
0.4415 0.36190
0.4425 0.36174
0.4435 0.36158
0.4445 0.36141
0.4455 0.36125
0.4465 0.36109
0.4475 0.36093
0.4485 0.36077
0.4495 0.36061
0.4505 0.36045
0.4515 0.36028
0.4525 0.36012
0.4535 0.35996
0.4545 0.35979
0.4555 0.35963
0.4565 0.35947
0.4575 0.35930
0.4585 0.35914
0.4595 0.35897
0.4605 0.35881
0.4615 0.35864
0.4625 0.35848
0.4635 0.35831
0.4645 0.35814
0.4655 0.35798
0.4665 0.35781
0.4675 0.35764
0.4685 0.35748
0.4695 0.35731
0.4705 0.35714
0.4715 0.35697
0.4725 0.35680
0.4735 0.35664
0.4745 0.35647
0.4755 0.35630
0.4765 0.35613
0.4775 0.35596
0.4785 0.35579
0.4795 0.35562
0.4805 0.35545
0.4815 0.35528
0.4825 0.35511
0.4835 0.35493
0.4845 0.35476
0.4855 0.35459
0.4865 0.35442
0.4875 0.35424
0.4885 0.35407
0.4895 0.35390
0.4905 0.35373
0.4915 0.35355
0.4925 0.35338
0.4935 0.35320
0.4945 0.35303
0.4955 0.35285
0.4965 0.35268
0.4975 0.35250
0.4985 0.35233
0.4995 0.35215
0.5005 0.35198
0.5015 0.35180
0.5025 0.35162
0.5035 0.35145
0.5045 0.35127
0.5055 0.35109
0.5065 0.35092
0.5075 0.35074
0.5085 0.35056
0.5095 0.35038
0.5105 0.35020
0.5115 0.35002
0.5125 0.34984
0.5135 0.34967
0.5145 0.34949
0.5155 0.34931
0.5165 0.34913
0.5175 0.34894
0.5185 0.34876
0.5195 0.34858
0.5205 0.34840
0.5215 0.34822
0.5225 0.34804
0.5235 0.34786
0.5245 0.34767
0.5255 0.34749
0.5265 0.34731
0.5275 0.34713
0.5285 0.34694
0.5295 0.34676
0.5305 0.34658
0.5315 0.34639
0.5325 0.34621
0.5335 0.34602
0.5345 0.34584
0.5355 0.34565
0.5365 0.34547
0.5375 0.34528
0.5385 0.34510
0.5395 0.34491
0.5405 0.34472
0.5415 0.34454
0.5425 0.34435
0.5435 0.34416
0.5445 0.34398
0.5455 0.34379
0.5465 0.34360
0.5475 0.34341
0.5485 0.34323
0.5495 0.34304
0.5505 0.34285
0.5515 0.34266
0.5525 0.34247
0.5535 0.34228
0.5545 0.34209
0.5555 0.34190
0.5565 0.34171
0.5575 0.34152
0.5585 0.34133
0.5595 0.34114
0.5605 0.34095
0.5615 0.34076
0.5625 0.34057
0.5635 0.34038
0.5645 0.34018
0.5655 0.33999
0.5665 0.33980
0.5675 0.33961
0.5685 0.33941
0.5695 0.33922
0.5705 0.33903
0.5715 0.33883
0.5725 0.33864
0.5735 0.33845
0.5745 0.33825
0.5755 0.33806
0.5765 0.33786
0.5775 0.33767
0.5785 0.33747
0.5795 0.33728
0.5805 0.33708
0.5815 0.33689
0.5825 0.33669
0.5835 0.33649
0.5845 0.33630
0.5855 0.33610
0.5865 0.33590
0.5875 0.33571
0.5885 0.33551
0.5895 0.33531
0.5905 0.33511
0.5915 0.33492
0.5925 0.33472
0.5935 0.33452
0.5945 0.33432
0.5955 0.33412
0.5965 0.33392
0.5975 0.33372
0.5985 0.33352
0.5995 0.33332
0.6005 0.33312
0.6015 0.33292
0.6025 0.33272
0.6035 0.33252
0.6045 0.33232
0.6055 0.33212
0.6065 0.33192
0.6075 0.33172
0.6085 0.33152
0.6095 0.33132
0.6105 0.33111
0.6115 0.33091
0.6125 0.33071
0.6135 0.33051
0.6145 0.33030
0.6155 0.33010
0.6165 0.32990
0.6175 0.32969
0.6185 0.32949
0.6195 0.32929
0.6205 0.32908
0.6215 0.32888
0.6225 0.32867
0.6235 0.32847
0.6245 0.32826
0.6255 0.32806
0.6265 0.32785
0.6275 0.32765
0.6285 0.32744
0.6295 0.32724
0.6305 0.32703
0.6315 0.32682
0.6325 0.32662
0.6335 0.32641
0.6345 0.32620
0.6355 0.32600
0.6365 0.32579
0.6375 0.32558
0.6385 0.32537
0.6395 0.32517
0.6405 0.32496
0.6415 0.32475
0.6425 0.32454
0.6435 0.32433
0.6445 0.32412
0.6455 0.32392
0.6465 0.32371
0.6475 0.32350
0.6485 0.32329
0.6495 0.32308
0.6505 0.32287
0.6515 0.32266
0.6525 0.32245
0.6535 0.32224
0.6545 0.32203
0.6555 0.32181
0.6565 0.32160
0.6575 0.32139
0.6585 0.32118
0.6595 0.32097
0.6605 0.32076
0.6615 0.32055
0.6625 0.32033
0.6635 0.32012
0.6645 0.31991
0.6655 0.31970
0.6665 0.31948
0.6675 0.31927
0.6685 0.31906
0.6695 0.31884
0.6705 0.31863
0.6715 0.31842
0.6725 0.31820
0.6735 0.31799
0.6745 0.31777
0.6755 0.31756
0.6765 0.31735
0.6775 0.31713
0.6785 0.31692
0.6795 0.31670
0.6805 0.31649
0.6815 0.31627
0.6825 0.31605
0.6835 0.31584
0.6845 0.31562
0.6855 0.31541
0.6865 0.31519
0.6875 0.31497
0.6885 0.31476
0.6895 0.31454
0.6905 0.31432
0.6915 0.31411
0.6925 0.31389
0.6935 0.31367
0.6945 0.31345
0.6955 0.31324
0.6965 0.31302
0.6975 0.31280
0.6985 0.31258
0.6995 0.31236
0.7005 0.31214
0.7015 0.31193
0.7025 0.31171
0.7035 0.31149
0.7045 0.31127
0.7055 0.31105
0.7065 0.31083
0.7075 0.31061
0.7085 0.31039
0.7095 0.31017
0.7105 0.30995
0.7115 0.30973
0.7125 0.30951
0.7135 0.30929
0.7145 0.30907
0.7155 0.30885
0.7165 0.30863
0.7175 0.30840
0.7185 0.30818
0.7195 0.30796
0.7205 0.30774
0.7215 0.30752
0.7225 0.30730
0.7235 0.30707
0.7245 0.30685
0.7255 0.30663
0.7265 0.30641
0.7275 0.30618
0.7285 0.30596
0.7295 0.30574
0.7305 0.30552
0.7315 0.30529
0.7325 0.30507
0.7335 0.30485
0.7345 0.30462
0.7355 0.30440
0.7365 0.30417
0.7375 0.30395
0.7385 0.30373
0.7395 0.30350
0.7405 0.30328
0.7415 0.30305
0.7425 0.30283
0.7435 0.30260
0.7445 0.30238
0.7455 0.30215
0.7465 0.30193
0.7475 0.30170
0.7485 0.30148
0.7495 0.30125
0.7505 0.30102
0.7515 0.30080
0.7525 0.30057
0.7535 0.30035
0.7545 0.30012
0.7555 0.29989
0.7565 0.29967
0.7575 0.29944
0.7585 0.29921
0.7595 0.29899
0.7605 0.29876
0.7615 0.29853
0.7625 0.29830
0.7635 0.29808
0.7645 0.29785
0.7655 0.29762
0.7665 0.29739
0.7675 0.29717
0.7685 0.29694
0.7695 0.29671
0.7705 0.29648
0.7715 0.29625
0.7725 0.29602
0.7735 0.29579
0.7745 0.29557
0.7755 0.29534
0.7765 0.29511
0.7775 0.29488
0.7785 0.29465
0.7795 0.29442
0.7805 0.29419
0.7815 0.29396
0.7825 0.29373
0.7835 0.29350
0.7845 0.29327
0.7855 0.29304
0.7865 0.29281
0.7875 0.29258
0.7885 0.29235
0.7895 0.29212
0.7905 0.29189
0.7915 0.29166
0.7925 0.29143
0.7935 0.29120
0.7945 0.29096
0.7955 0.29073
0.7965 0.29050
0.7975 0.29027
0.7985 0.29004
0.7995 0.28981
0.8005 0.28958
0.8015 0.28934
0.8025 0.28911
0.8035 0.28888
0.8045 0.28865
0.8055 0.28842
0.8065 0.28818
0.8075 0.28795
0.8085 0.28772
0.8095 0.28749
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