Spreadsheet: 52159d1251876757-how-to-integrate-the-force-vs-time-history-integration-function
Sheet: Sheet2

Test 12
Time (s) | Force (kN) | Force (N) | Trapezoid Rule | Trapezoid Rule
0.0789187472424879 | 0 | 0 | 0.0001766553740841799 | 1.766553740841799e-07 | 0 | 0.0001766553740836456 | -2489.607432502035 | -2489.607432502035
0.0789363473199283 | 0.020074386 | 20.074386 | 0.001307249782296809 | 1.307249782296809e-06 | 1.76000774403407e-05 | 0.001307249782299046 | -2487.095000483785 | -2487.095000483785
0.0789539473973686 | 0.128476072 | 128.476072 | 0.003285789996667781 | 3.285789996667781e-06 | 3.52001548806815e-05 | 0.003285789996675979 | -2482.698244451849 | -2482.698244451849
0.0789715474748089 | 0.244907512 | 244.907512 | 0.005052343755127794 | 5.052343755127794e-06 | 5.28002323210222e-05 | 0.005052343755112539 | -2478.772569433049 | -2478.77256943305
0.0789891475522493 | 0.329219934 | 329.219934 | 0.005970951707372603 | 5.970951707372603e-06 | 7.0400309761363e-05 | 0.0059709517073875 | -2476.731218428061 | -2476.731218428061
0.0790067476296896 | 0.34929432 | 349.29432 | 0.006147607081494587 | 6.147607081494588e-06 | 8.80003872017037e-05 | 0.006147607081471008 | -2476.338650930012 | -2476.338650930012
0.07902434770713 | 0.34929432 | 349.29432 | 0.005900289552459298 | 5.900289552459299e-06 | 0.000105600464642044 | 0.005900289552474115 | -2476.88824543898 | -2476.88824543898
0.0790419477845703 | 0.321190179 | 321.190179 | 0.005264330202239745 | 5.264330202239745e-06 | 0.000123200542082385 | 0.005264330202252968 | -2478.301488439467 | -2478.301488439467
0.0790595478620106 | 0.27702653 | 277.02653 | 0.004169066875910143 | 4.169066875910143e-06 | 0.000140800619522726 | 0.004169066875894085 | -2480.735406942422 | -2480.735406942422
0.079077147939451 | 0.196728985 | 196.728985 | 0.003073803540727904 | 3.073803540727904e-06 | 0.000158400696963066 | 0.003073803540735625 | -2483.169325465049 | -2483.169325465049
0.0790947480168913 | 0.152565335 | 152.565335 | 0.002932479239717518 | 2.932479239717518e-06 | 0.000176000774403407 | 0.002932479239708698 | -2483.483379467295 | -2483.483379467295
0.0791123480943317 | 0.180669476 | 180.669476 | 0.004169066875887131 | 4.169066875887131e-06 | 0.000193600851843748 | 0.004169066875894316 | -2480.735406942473 | -2480.735406942473
0.079129948171772 | 0.293086039 | 293.086039 | 0.006112276008399174 | 6.112276008399175e-06 | 0.000211200929284089 | 0.00611227600841418 | -2476.417164425779 | -2476.41716442578
0.0791475482492123 | 0.401487724 | 401.487724 | 0.007384194708879039 | 7.384194708879039e-06 | 0.000228801006724429 | 0.007384194708856818 | -2473.590678424713 | -2473.590678424713
0.0791651483266527 | 0.437621619 | 437.621619 | 0.00763151223784081 | 7.63151223784081e-06 | 0.00024640108416477 | 0.007631512237853973 | -2473.041083915909 | -2473.041083915909
0.079182748404093 | 0.429591865 | 429.591865 | 0.007454856863792734 | 7.454856863792733e-06 | 0.000264001161605111 | 0.0074548568637703 | -2473.433651413794 | -2473.433651413794
0.0792003484815334 | 0.417547233 | 417.547233 | 0.007101546106785137 | 7.101546106785138e-06 | 0.000281601239045452 | 0.007101546106802592 | -2474.218786429366 | -2474.218786429366
0.0792179485589737 | 0.389443092 | 389.443092 | 0.00639492460165228 | 6.39492460165228e-06 | 0.000299201316485792 | 0.006394924601668333 | -2475.789056440773 | -2475.789056440773
0.079235548636414 | 0.337249688 | 337.249688 | 0.005440985576357272 | 5.440985576357272e-06 | 0.000316801393926133 | 0.005440985576336626 | -2477.908920941428 | -2477.908920941428
0.0792531487138544 | 0.281041407 | 281.041407 | 0.004769695153046765 | 4.769695153046764e-06 | 0.000334401471366474 | 0.004769695153058738 | -2479.400677437674 | -2479.400677437674
0.0792707487912947 | 0.260967021 | 260.967021 | 0.005087674828188633 | 5.087674828188634e-06 | 0.000352001548806815 | 0.00508767482816903 | -2478.694055937358 | -2478.694055937358
0.0792883488687351 | 0.317175302 | 317.175302 | 0.006253600309425746 | 6.253600309425746e-06 | 0.000369601626247155 | 0.006253600309441464 | -2476.103110423498 | -2476.103110423498
0.0793059489461754 | 0.39345797 | 393.45797 | 0.00717220826173803 | 7.172208261738031e-06 | 0.000387201703687496 | 0.007172208261716447 | -2474.06175941836 | -2474.06175941836
0.0793235490236158 | 0.42156211 | 421.56211 | 0.007454856863751586 | 7.454856863751586e-06 | 0.000404801781127837 | 0.007454856863770323 | -2473.433651413885 | -2473.433651413885
0.0793411491010561 | 0.425576988 | 425.576988 | 0.007702174392754169 | 7.70217439275417e-06 | 0.000422401858568178 | 0.007702174392767431 | -2472.884056904991 | -2472.884056904991
0.0793587491784964 | 0.449666251 | 449.666251 | 0.00823214051504315 | 8.232140515043149e-06 | 0.000440001936008519 | 0.00823214051501792 | -2471.706354411015 | -2471.706354411015
0.0793763492559368 | 0.485800146 | 485.800146 | 0.008444126962137548 | 8.444126962137548e-06 | 0.000457602013448859 | 0.00844412696215877 | -2471.235273417472 | -2471.235273417472
0.0793939493333771 | 0.473755514 | 473.755514 | 0.007772836538910395 | 7.772836538910394e-06 | 0.0004752020908892 | 0.007772836538880899 | -2472.727029913533 | -2472.727029913533
0.0794115494108175 | 0.409517479 | 409.517479 | 0.0067835664404754 | 6.7835664404754e-06 | 0.000492802168329541 | 0.006783566440492408 | -2474.925407910055 | -2474.925407910055
0.0794291494882578 | 0.361338952 | 361.338952 | 0.006465586756565584 | 6.465586756565584e-06 | 0.000510402245769882 | 0.006465586756581477 | -2475.632029429854 | -2475.632029429855
0.0794467495656981 | 0.373383583 | 373.383583 | 0.007030883960716223 | 7.030883960716223e-06 | 0.000528002323210222 | 0.007030883960689543 | -2474.37581342063 | -2474.37581342063
0.0794643496431385 | 0.425576988 | 425.576988 | 0.008302802669911017 | 8.302802669911016e-06 | 0.000545602400650563 | 0.008302802669931834 | -2471.549327400198 | -2471.549327400198
0.0794819497205788 | 0.517919164 | 517.919164 | 0.01021068072942607 | 1.021068072942607e-05 | 0.000563202478090904 | 0.01021068072939538 | -2467.309598379053 | -2467.309598379054
0.0794995497980192 | 0.642380359 | 642.380359 | 0.01271918706600136 | 1.271918706600136e-05 | 0.000580802555531245 | 0.01271918706602259 | -2461.73513985333 | -2461.735139853331
0.0795171498754595 | 0.802975448 | 802.975448 | 0.01554567307772273 | 1.554567307772273e-05 | 0.000598402632971585 | 0.0155456730777618 | -2455.454059827283 | -2455.454059827283
0.0795347499528998 | 0.963570538 | 963.570538 | 0.01791285511341664 | 1.791285511341664e-05 | 0.000616002710411926 | 0.01791285511336268 | -2450.193655303518 | -2450.193655303519
0.0795523500303402 | 1.071972223 | 1071.972223 | 0.01907878059458698 | 1.907878059458698e-05 | 0.000633602787852267 | 0.01907878059463493 | -2447.602709789807 | -2447.602709789807
0.0795699501077805 | 1.096061487 | 1096.061487 | 0.01904344952165047 | 1.904344952165047e-05 | 0.000651202865292608 | 0.01904344952157715 | -2447.681223285221 | -2447.681223285221
0.0795875501852209 | 1.067957346 | 1067.957346 | 0.01830149694334085 | 1.830149694334085e-05 | 0.000668802942732948 | 0.01830149694338674 | -2449.330006792576 | -2449.330006792576
0.0796051502626612 | 1.011749065 | 1011.749065 | 0.01717090253512828 | 1.717090253512828e-05 | 0.000686403020173289 | 0.01717090253517144 | -2451.842438810826 | -2451.842438810826
0.0796227503401015 | 0.939481274 | 939.481274 | 0.0162522945829581 | 1.62522945829581e-05 | 0.00070400309761363 | 0.01625229458289643 | -2453.883789815648 | -2453.883789815648
0.0796403504175419 | 0.907362257 | 907.362257 | 0.01589898383468917 | 1.589898383468917e-05 | 0.000721603175053971 | 0.01589898383472815 | -2454.668924811802 | -2454.668924811802
0.0796579504949822 | 0.899332502 | 899.332502 | 0.01607563920886111 | 1.607563920886111e-05 | 0.000739203252494311 | 0.01607563920881279 | -2454.276357313642 | -2454.276357313642
0.0796755505724226 | 0.927436643 | 927.436643 | 0.01667626748594845 | 1.667626748594845e-05 | 0.000756803329934652 | 0.01667626748597721 | -2452.941627809003 | -2452.941627809004
0.0796931506498629 | 0.967585415 | 967.5854149999999 | 0.01724156469013675 | 1.724156469013675e-05 | 0.000774403407374993 | 0.01724156469008492 | -2451.685411799696 | -2451.685411799696
0.0797107507273033 | 0.991674679 | 991.674679 | 0.01745355114598146 | 1.745355114598146e-05 | 0.000792003484815334 | 0.01745355114602425 | -2451.214330786708 | -2451.214330786708
0.0797283508047436 | 0.991674679 | 991.674679 | 0.01738288899108186 | 1.738288899108186e-05 | 0.000809603562255674 | 0.01738288899111184 | -2451.371357797596 | -2451.371357797596
0.0797459508821839 | 0.983644924 | 983.6449240000001 | 0.01720623360827988 | 1.720623360827988e-05 | 0.000827203639696015 | 0.01720623360822816 | -2451.763925314934 | -2451.763925314934
0.0797635509596243 | 0.971600292 | 971.600292 | 0.01713557146207165 | 1.713557146207164e-05 | 0.000844803717136356 | 0.01713557146211461 | -2451.920952306507 | -2451.920952306508
0.0797811510370646 | 0.97561517 | 975.6151699999999 | 0.01710024038912288 | 1.710024038912288e-05 | 0.000862403794576697 | 0.01710024038905799 | -2451.999465801949 | -2451.999465801949
0.079798751114505 | 0.967585415 | 967.5854149999999 | 0.01692358500613177 | 1.692358500613177e-05 | 0.000880003872017038 | 0.01692358500617337 | -2452.392033319707 | -2452.392033319707
0.0798163511919453 | 0.955540783 | 955.540783 | 0.01667626747713526 | 1.667626747713526e-05 | 0.000897603949457378 | 0.01667626747717717 | -2452.941627828588 | -2452.941627828588
0.0798339512693856 | 0.939481274 | 939.481274 | 0.01604030812701689 | 1.604030812701689e-05 | 0.000915204026897719 | 0.01604030812695592 | -2454.354870828851 | -2454.354870828852
0.079851551346826 | 0.883272993 | 883.2729929999999 | 0.0148743826456465 | 1.48743826456465e-05 | 0.00093280410433806 | 0.01487438264568389 | -2456.945816343008 | -2456.945816343008
0.0798691514242663 | 0.806990325 | 806.990325 | 0.01388511253853714 | 1.388511253853714e-05 | 0.000950404181778401 | 0.01388511253849463 | -2459.144194358807 | -2459.144194358807
0.0798867515017067 | 0.77085643 | 770.85643 | 0.01381445039235813 | 1.381445039235813e-05 | 0.000968004259218741 | 0.01381445039238195 | -2459.301221350315 | -2459.301221350316
0.079904351579147 | 0.798960571 | 798.960571 | 0.01427375436848358 | 1.427375436848358e-05 | 0.000985604336659082 | 0.01427375436851699 | -2458.280545847814 | -2458.280545847814
0.0799219516565873 | 0.823049834 | 823.049834 | 0.01437974759653289 | 1.437974759653289e-05 | 0.00100320441409942 | 0.01437974759648878 | -2458.045005341038 | -2458.045005341038
0.0799395517340277 | 0.811005203 | 811.005203 | 0.01384978147420391 | 1.38497814742039e-05 | 0.00102080449153976 | 0.01384978147423786 | -2459.222707835102 | -2459.222707835102
0.079957151811468 | 0.762826676 | 762.826676 | 0.01335514641629513 | 1.335514641629513e-05 | 0.0010384045689801 | 0.01335514641624379 | -2460.321896852678 | -2460.321896852678
0.0799747518889084 | 0.754796921 | 754.796921 | 0.01342580856232415 | 1.342580856232415e-05 | 0.00105600464642044 | 0.01342580856235707 | -2460.164869861502 | -2460.164869861502
0.0799923519663487 | 0.77085643 | 770.85643 | 0.01363779501826403 | 1.363779501826403e-05 | 0.00107360472386078 | 0.01363779501829746 | -2459.693788848302 | -2459.693788848303
0.080009952043789 | 0.778886185 | 778.886185 | 0.01377911931937752 | 1.377911931937752e-05 | 0.00109120480130112 | 0.01377911931932438 | -2459.379734845828 | -2459.379734845828
0.0800275521212294 | 0.786915939 | 786.915939 | 0.01416776114051364 | 1.416776114051364e-05 | 0.00110880487874146 | 0.01416776114054855 | -2458.516086354414 | -2458.516086354415
0.0800451521986697 | 0.823049834 | 823.049834 | 0.01505103801981278 | 1.505103801981278e-05 | 0.0011264049561818 | 0.01505103801976661 | -2456.553248844861 | -2456.553248844861
0.0800627522761101 | 0.88728787 | 887.28787 | 0.01632295672898172 | 1.632295672898172e-05 | 0.00114400503362214 | 0.01632295672901812 | -2453.726762824485 | -2453.726762824485
0.0800803523535504 | 0.967585415 | 967.5854149999999 | 0.01752421329219145 | 1.752421329219145e-05 | 0.00116160511106249 | 0.01752421329213769 | -2451.05730379513 | -2451.05730379513
0.0800979524309908 | 1.023793697 | 1023.793697 | 0.01833682802519752 | 1.833682802519752e-05 | 0.00117920518850283 | 0.0183368280252427 | -2449.251493277339 | -2449.251493277339
0.0801155525084311 | 1.059927592 | 1059.927592 | 0.01904344952154536 | 1.904344952154536e-05 | 0.00119680526594317 | 0.01904344952157704 | -2447.681223285455 | -2447.681223285455
0.0801331525858714 | 1.104091241 | 1104.091241 | 0.01960874672574486 | 1.960874672574486e-05 | 0.00121440534338351 | 0.01960874672568471 | -2446.425007276122 | -2446.425007276123
0.0801507526633118 | 1.124165628 | 1124.165628 | 0.01957341565258 | 1.957341565258e-05 | 0.00123200542082385 | 0.01957341565262823 | -2446.503520772044 | -2446.503520772045
0.0801683527407521 | 1.100076364 | 1100.076364 | 0.01869013877336393 | 1.869013877336393e-05 | 0.00124960549826419 | 0.01869013877340976 | -2448.466358281414 | -2448.466358281414
0.0801859528181924 | 1.023793697 | 1023.793697 | 0.0172768957632072 | 1.72768957632072e-05 | 0.00126720557570453 | 0.01727689576314058 | -2451.606898303984 | -2451.606898303984
0.0802035528956328 | 0.939481274 | 939.481274 | 0.01600497705385907 | 1.600497705385907e-05 | 0.00128480565314487 | 0.01600497705389832 | -2454.433384324758 | -2454.433384324758
0.0802211529730731 | 0.879258116 | 879.2581160000001 | 0.01508636910168154 | 1.508636910168154e-05 | 0.00130240573058521 | 0.01508636910162355 | -2456.474735329597 | -2456.474735329597
0.0802387530505135 | 0.835094466 | 835.094466 | 0.01441507866951015 | 1.441507866951015e-05 | 0.00132000580802555 | 0.01441507866954549 | -2457.966491845533 | -2457.966491845533
0.0802563531279538 | 0.802975448 | 802.975448 | 0.01413243006753501 | 1.413243006753501e-05 | 0.00133760588546589 | 0.01413243006749166 | -2458.594599849922 | -2458.594599849922
0.0802739532053942 | 0.802975448 | 802.975448 | 0.01462706512545003 | 1.462706512545003e-05 | 0.00135520596290623 | 0.01462706512548589 | -2457.495410832333 | -2457.495410832333
0.0802915532828345 | 0.85918373 | 859.1837300000001 | 0.01554567308653502 | 1.554567308653502e-05 | 0.00137280604034657 | 0.01554567308656988 | -2455.4540598077 | -2455.4540598077
0.0803091533602748 | 0.907362257 | 907.362257 | 0.01593431490783375 | 1.593431490783376e-05 | 0.00139040611778692 | 0.01593431490778487 | -2454.590411315925 | -2454.590411315925
0.0803267534377152 | 0.903347379 | 903.3473789999999 | 0.01540434877669615 | 1.540434877669615e-05 | 0.00140800619522726 | 0.01540434877673392 | -2455.768113829564 | -2455.768113829564
0.0803443535151555 | 0.847139098 | 847.139098 | 0.01420309222245991 | 1.420309222245991e-05 | 0.0014256062726676 | 0.01420309222240531 | -2458.437572838978 | -2458.437572838978
0.0803619535925959 | 0.766841553 | 766.841553 | 0.01289584244007454 | 1.289584244007454e-05 | 0.00144320635010794 | 0.01289584244010615 | -2461.34257235539 | -2461.34257235539
0.0803795536700362 | 0.69858864 | 698.5886399999999 | 0.0116945858857487 | 1.16945858857487e-05 | 0.00146080642754828 | 0.01169458588577737 | -2464.012031365003 | -2464.012031365003
0.0803971537474765 | 0.630335727 | 630.3357269999999 | 0.0104226671765753 | 1.04226671765753e-05 | 0.00147840650498862 | 0.01042266717653511 | -2466.838517385388 | -2466.838517385389
0.0804147538249169 | 0.554053059 | 554.053059 | 0.009292072768296978 | 9.292072768296978e-06 | 0.00149600658242896 | 0.009292072768319875 | -2469.350949403784 | -2469.350949403784
0.0804323539023572 | 0.501859655 | 501.859655 | 0.00872677556423886 | 8.726775564238859e-06 | 0.0015136066598693 | 0.008726775564212088 | -2470.607165412803 | -2470.607165412803
0.0804499539797976 | 0.489815023 | 489.815023 | 0.008726775564197573 | 8.726775564197573e-06 | 0.00153120673730964 | 0.008726775564212088 | -2470.607165412894 | -2470.607165412895
0.0804675540572379 | 0.501859655 | 501.859655 | 0.008797437719103997 | 8.797437719103997e-06 | 0.00154880681474998 | 0.008797437719125566 | -2470.450138401991 | -2470.450138401991
0.0804851541346782 | 0.497844778 | 497.844778 | 0.008585451272011546 | 8.585451272011546e-06 | 0.00156640689219032 | 0.008585451271985314 | -2470.92121939553 | -2470.92121939553
0.0805027542121186 | 0.477770392 | 477.770392 | 0.008267471596854382 | 8.267471596854383e-06 | 0.00158400696963066 | 0.008267471596874652 | -2471.627840895879 | -2471.627840895879
0.0805203542895589 | 0.461710883 | 461.710883 | 0.008161478368935927 | 8.161478368935928e-06 | 0.001601607047071 | 0.00816147836890908 | -2471.863381402365 | -2471.863381402365
0.0805379543669993 | 0.46572576 | 465.72576 | 0.008090816213971138 | 8.090816213971138e-06 | 0.00161920712451135 | 0.008090816213991074 | -2472.020408413397 | -2472.020408413397
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0.081558758858539 | 0.120446317 | 120.446317 | 0.003144465686861006 | 3.144465686861006e-06 | 0.00262241153861077 | 0.003144465686848919 | -2483.012298473642 | -2483.012298473642
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0.0815939590134197 | 0.112416563 | 112.416563 | 0.001978540214382924 | 1.978540214382923e-06 | 0.00265761169349145 | 0.001978540214376878 | -2485.603243968038 | -2485.603243968038
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0.0816291591683004 | 0.104386808 | 104.386808 | 0.001907878059460202 | 1.907878059460202e-06 | 0.00269281184837213 | 0.001907878059463352 | -2485.760270978977 | -2485.760270978978
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0.0816643593231811 | 0.092342177 | 92.34217699999999 | 0.001625229466205593 | 1.625229466205593e-06 | 0.00272801200325281 | 0.001625229466209558 | -2486.388378963988 | -2486.388378963988
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0.0817171595555021 | 0.080297545 | 80.297545 | 0.001377911937209083 | 1.377911937209083e-06 | 0.00278081223557384 | 0.001377911937212444 | -2486.937973472869 | -2486.937973472869
0.0817347596329424 | 0.076282668 | 76.282668 | 0.001342580864160919 | 1.342580864160919e-06 | 0.00279841231301418 | 0.001342580864155758 | -2487.016486968531 | -2487.016486968531
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0.0817699597878231 | 0.076282668 | 76.282668 | 0.001307249782302993 | 1.307249782302993e-06 | 0.00283361246789486 | 0.001307249782298967 | -2487.095000483771 | -2487.095000483771
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0.0818227600201441 | 0.068252913 | 68.25291299999999 | 0.001236587627389298 | 1.236587627389298e-06 | 0.00288641270021588 | 0.001236587627385489 | -2487.252027494691 | -2487.252027494691
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0.0819987607945476 | 0.016059509 | 16.059509 | 0.0002119864471398381 | 2.119864471398381e-07 | 0.00306241347461929 | 0.0002119864471403604 | -2489.528919006356 | -2489.528919006356
0.0820163608719879 | 0.008029754 | 8.029754 | 0.0001059932191699833 | 1.059932191699833e-07 | 0.00308001355205963 | 0.0001059932191701583 | -2489.764459512955 | -2489.764459512955
0.0820339609494282 | 0.004014877 | 4.014877 | 3.533107305682824e-05 | 3.533107305682824e-08 | 0.00309761362949997 | 3.533107305672029e-05 | -2489.921486504318 | -2489.921486504319
0.0820515610268686 | 0 | 0 |  |  | 0.00311521370694031 | 0
 |  |  |  |  | 0.00313281378438065 | #N/A
 | Area |  | 1.432781091733588 |  | 0.00315041386182099 | #N/A
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 |  |  |  |  | 0.00360801587526985 | 0
 |  |  |  |  | 0.00362561595271019 | 0
 |  |  |  |  | 0.00364321603015053 | 0
 |  |  |  |  | 0.00366081610759087 | 0
 |  |  |  |  | 0.00367841618503121 | 0
 |  |  |  |  | 0.00369601626247155 | 0
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