Kodi integral, ndipo kodi tanthauzo lake thupi

The anali kuoneka mfundo yofunika chifukwa chosowa cha kupeza ntchito wosazindikira wa otumphukira ake, ndi kudziwa phindu la ntchito m'dera akalumikidzidwa zovuta, mtunda anayenda mtunda, ndi magawo zili zokhotakhota ndi maikwezhoni osalunjika.

kumene ndi sayansi tikudziwa kuti ntchito ndi mankhwala a mphamvu pa mtunda. Ngati gulu onse ali pa liwiro zonse kapena mtunda wagonjetsedwa ndi kugwiritsa ntchito mphamvu, ndiye chirichonse chiri bwino, chabe zikuchulukireni. ndi yofunika kwambiri pa zonse ndi chiani? Izi ndi liniya ntchito ya mtundu Y = Kx + c.

Koma mphamvu ya ntchito zosiyanasiyana ndipo ena ubwenzi mwadongosolo. Ndi mmenenso zilili ndi mawerengedwe a mtunda ulendo, ngati liwiro si nthawi zonse.

Choncho, n'zomveka chifukwa pali yofunika. Liwulo ngati mtengo wa mankhwala a mfundo za ntchito pa increment n'zochepa mfundo kwathunthu limafotokoza tanthauzo lenileni yaikulu akuti ngati dera zimakwana njanjira ndi mzere pamwamba pa ntchito, ndi m'mbali - tanthauzo la malire.

Jean Gaston Darboux, French masamu, mu theka lachiwiri la m'ma XIX momveka bwino kwambiri kuti ichi yofunika. Iye anapanga izo momveka bwino kuti lonse sadzakhala ndi ovuta kuwamvetsa ngakhale sukulu junior sekondale pa nkhani imeneyi.

Tiyerekeze pali ntchito ya mawonekedwe aliwonse. Y-olamulira, pa amene waikamo mtengo wa mkanganowo, lagawidwa intervals yaing'ono, Choncho, iwo ali wamphamvu kakang'ono, koma chifukwa maganizo osawerengeka ndi umboni ndithu, ndi wokwanira kulingalira zidutswa chabe, kuchuluka kwa zomwe kawirikawiri amaimira kalata Greek Δ (ankadziwana).

Chithunzichi anali "sliced" mu midadada ang'onoang'ono.

Aliyense mtengo wa mkanganowo limafanana ndi mfundo pa kukhazikitsa olamulira pa zomwe anakaika mfundo lolingana a kugwira ntchito. Koma ngati malire mu anasankha dera ziwiri, mfundo ndi ntchito kudzakhala awiri kapena ndi zochepa.

Uwerenge mankhwala a mfundo zikuluzikulu za increment Δ otchedwa Darboux wambirimbiri, ndipo amatchedwa S. Choncho, mfundo zing'onozing'ono m'dera yochepa, kuchulukitsa ndi Δ, pamodzi kupanga pang'ono Darboux m. malo palokha akufanana ndi trapezoid amakona anayi, kotero ngati ntchito ya kupindika mzere chifukwa ndi increment kakang'ono akhoza kuwasamalira. Chophweka njira kupeza kuderali zojambula chithunzi - zidutswa apangidwe kwa mfundo zikuluzikulu ndi ang'onoang'ono a ntchito pa Δ-increment ndi ogaŵikana awiri, kuti limanenedwa ngati zikutanthauza masamu.

Ndicho chimene yofunika Darboux:

m = Σf (x) Δ - pang'ono;

S = Σf (× + Δ) Δ - wambirimbiri.

Choncho, kodi yofunika? Area njanjira ndi mzere ntchito ndi tanthauzo la malire adzakhala wofanana:

∫f (x) dx = {(S + s) / 2} + m'ma

Ndiko kuti, zikutanthauza masamu a zazikulu ndi zazing'ono ndalama Darbu.s - phindu zonse, resettable pa zosiyanasiyana.

Zochokera mawu zojambula za mfundo imeneyi, zimaonekeratu tanthauzo thupi la yofunika. akalumikidzidwa Square, ndondomeko ya ntchito ya liwiro, ndi zochepa nthawi imeneyi pa x-olamulira adzakhala kutalika kwa kutalika kwa ulendo.

L = ∫f (x) dx mu imeneyi kwa T1 kuti t2,

kumene

f (x) - ntchito ya liwiro, kuti ndi chilinganizo chimene chingasinthe pa nthawi;

L - kutalika kwa njira;

T1 - chiyambi nthawi ya njira;

t2 - nthawi akamaliza njira.

Chimodzimodzi zomwezo anatsimikiza ndi kuchuluka kwa ntchito, koma adzakhala anakaika pa abscissa mtunda ndi kukhazikitsa - kuchuluka kwa mphamvu amagwiritsa ntchito pa mfundo iliyonse payekha.