Page 367 - Srednje skole - radovi

INTEGRALI
INTEGRALS

Autor: MILICA MATORĈEVIĆ, II , Srednja škola, Grocka
2
Mentor: VIOLETA KOMNENOVIĆ, profesor matematike, Elektrotehniĉka škola „ Nikola
Tesla“, Beograd
REZIME

Integrali su jedan od najvaţnijih pojmova matematiĉke analize. Postoji više vrsta integrala, ali najpoznatiji
meĊu njima su neodreĊeni i odreĊeni integrali. Integralni raĉun zajedno sa diferencijalnim raĉunom stvara

infinitezimalni raĉun, koji predstavlja osnovnu konstrukciju za prirodne i tehniĉke nauke.

OdreĊeni integral je tesno povezan sa starim matematiĉkim problemom odreĊivanja površine figure
koja se nalazi ispod grafa. Taj problem pratio je matematiĉare sve do XVII veka kada su Njutn i Lajbnic

otkrili vezu izmeĊu odreĊenog i neodreĊenog integrala. Naime oni su otkrili da se površine ispod grafa mogu
izraĉunati obrnutim procesom diferencijacije. Danas integralni raĉun ima veliku primenu kako u matematici,

tako i u fizici, pa ĉak i u ekonomiji. Cilj mog rada bio je da saznam šta su to integrali i kakvu primenu imaju

u matematici.

Kljuĉne reĉi: odreĊeni integrali, neodreĊeni integrali, primena odreĊenih integrala, Njutn-

Lajbnicova formula.

SUMMARY

Integrals are one of the most important concepts of mathematical analysis. There are
several types of integrals, but the most famous among them are indefinite and definite integrals.

Integral calculus with differential calculus creates infinitesimal calculus, which is the basic
structure of science and technical science.

Definite integral is closely connected with old mathematical problem of determining the

area of the figure beneath the graph. This problem has followed all mathematicians until the
XVII century, when Newton and Leibniz discovered a link between definite and indefinite

integrals. Namely they found that the area under the graph can calculate the inverse process of

differentation. Today integral calculus has application both in mathematics and in physics, even
in economics. My aim was to find out what integrals are and what kind of application they have

in mathematics.

Key words: definite integrals, indefinite integrals, application of definite integrals, Newton-
Leibniz formula.