Yintoni ebalulekileyo, yaye yintoni na intsingiselo yalo ngokomzimba

Inkangeleko yaba ingqikelelo elipheleleyo ngenxa nemfuno yokufumana umsebenzi ukuzazi of ithe yayo, aqingqa ixabiso indawo yomsebenzi iimilo ezintsonkothileyo, umgama ohanjiweyo umgama, kunye parameters echazwe amagophe yi quadratic nonlinear.

Yebo kwaye yemvelo siyazi ukuba umsebenzi imveliso amandla phezu umgama. Ukuba yonke intshukumo ngesantya esingaguqukiyo okanye mgama ukoyisa kunye nesicelo bomkhosi enye, ngoko yonke into icacile, phinda nje. Yintoni ebalulekileyo njalo? Oku yomgama umsebenzi ifomu y = TE + c.

Kodwa ke amandla msebenzi azifani kwaye thile ngocwangco. Injalo kanye imeko ukubalwa umgama ohanjiweyo, ukuba isantya ayikho njalo.

Ngoko ke, siyaqondakala isizathu sokuba kukho ebalulekile. Ukuchaza njengento lodibaniso iimveliso amaxabiso umsebenzi phezu ukwenyuselwa omncane Kwempikiswano ichaza ngokupheleleyo intsingiselo eyintloko elide kummandla lo mzobo lingqongwe kumgca phezulu umsebenzi, kunye kungqameko - inkcazo imida.

Jean Gaston Darboux, ingcali yezibalo French, kwisiqingatha sesibini senkulungwane XIX kuchazwe ngokucacileyo ukuba lo ebalulekile. Wenza kwacaca ukuba kuya kuba nzima ukuba sikuqonde yesikolo junior kwisikolo aphezulu kulo mba lonke.

Masithi kukho umsebenzi nayiphi imilo ezintsonkothileyo. y-axis, apho ezifakwe ixabiso ingxabano, yahlulahlulwe amathuba amancinci, ngokuyinene, ukuba ngamabona ezincinane, kodwa ngenxa yokuba ingqikelelo Infinity kakhulu abstract, kwanele ukuba nomfanekiso iziqwenga nje encinane, imali leyo idla zibonakaliswe yileta Greek Δ (delta).

Lo mcimbi "zakhutshwa" phakathi zaziibloko ezincinane.

ixabiso ngalinye ingxabano uhambelana kwindawo esqwini Ukunxibelelanisa apho imali kumaxabiso ahambelanayo lo msebenzi. Kodwa njengoko imida kwi ariya ekhetiweyo ezimbini, iinqobo kunye nemisebenzi iya kuba ezimbini okanye ngaphezulu kwaye ngaphantsi.

Umdibaniso imveliso amaxabiso ezinkulu ngenxa ukwenyuselwa Δ ebizwa isixa esikhulu Darboux, yaye ubizwa ngokuba S. Ngoko, kunye amanani amancinane ukuba indawo elinganiselwe, iphindwe Δ, benza imali encinci Darboux s. Le sayithi ngokwayo ufana trapezoid ebuxande, ukuze njengomsebenzi ugobile selayini ngenxa ukwenyuselwa omncane ngayo nokungahoywa. Indlela elula yokufumana kummandla imilo zejiyometri - lamaqhosha elisongiweyo lwamaxabiso ezinkulu ezincinane le function Δ-ukwenyuselwa kwaye silahlule ngababini, ukuba luchazwa kwemin arithmetic.

Nantso into Darboux ebalulekile:

s = Σf (x) Δ - imali encinane;

S = Σf (x + Δ) Δ - mali esikhulu.

Ngoko ke, yintoni na ebalulekile? Area ongqongwe umsebenzi umgca and definition kwemida ziya kuba silingana:

∫f (x) DX = {(S + s) / 2} + c

Oko kukuthi, imin lokubala eliguqukayo iimali ezinkulu nezincinane Darbu.s - ixabiso rhoqo, resettable phezu iyantlukwano.

Ngokusekelwe ibinzana zejometri kolu luvo, kuye kucace intsingiselo ebonakalayo kwezi ebalulekile. iimilo Square, wachaza ukuba umsebenzi isantya, kunye limited kunelixesha lokuphumla kwi x-axis iya kuba ubude nomgama ohanjiweyo.

L = ∫f (x) DX kwi lokuphumla ukusuka T1 ukuya T2,

apho

f (x) - umsebenzi ngesantya, oko kukuthi ifomula eyenziwe ngawo itshintsha ngokuhamba kwexesha;

L - ubude umendo;

T1 - ixesha ekuqaleni indlela;

T2 - time sokugqitywa endleleni.

Kanye lo mgaqo umiselwa bomsebenzi, kodwa ziya kudipozithwa kwi abscissa kumgama kwaye iququzelele - isixa kwemikhosi bafakela ingongoma nganye ngamnye.