Applications Of Line Integrals

U ovom radu analiziramo pojam krivuljnih integrala i njihovu ključnu ulogu kako u matematičkoj analizi, tako i u primjenama unutar fizike. Navodimo njihove definicije, ključna svojstva te širok spektar primjena u različitim kontekstima. Na početku analiziramo krivuljni integral prve vrste, gdje definiramo ovu vrstu integrala i navodimo njegova svojstva i karakteristike. Zatim je naglasak stavljen na primjene krivuljnog integrala prve vrste, posebno unutar matematičkih i fizikalnih konteksta. Svaku od ovih primjena ilustriramo praktičnim primjerima kako bismo bolje razumjeli njihovu primjenu u stvarnom svijetu. Nakon toga, promatramo krivuljni integral druge vrste, njegovu definiciju, svojstva i karakteristike. Navodimo vezu krivuljnog integrala druge vrste s dvostrukim integralima, što je opisano u poznatom Greenovom teoremu. Na kraju analiziramo primjene krivuljnog integrala druge vrste kroz konkretne primjere, čime dodatno produbljujemo naše razumijevanje ovih pojmova.In this paper, we analyze the concept of line integrals and their pivotal role in both mathematical analysis and applications within physics. We explore their definitions, key properties, and a wide range of applications in various contexts. Our research commences with the analysis of the line integral of the first kind, where we will define this type of integral and investigate its properties and characteristics. Subsequently, the focus shifts to the applications of the line integral of the first kind, particularly within mathematical and physical contexts. Each of these applications is illustrated with practical examples to better understand their real-world relevance. Following that, we direct our attention to the line integral of the second kind, its definition, properties, and characteristics. After that, we explore how it is related to double integrals, as described in the well-known Green’s theorem. Finally, the research is concluded by analyzing the applications of the line integral of the second kind through concrete examples, further deepening our understanding of this concept