Republic of Panama Autonomous University of Chiriquí Faculty of Natural and Exact Sciences School of Physics Teacher: Johana Serrano Course: Scientific English Topic: Calculus- Differential and Integral. Prepared by: Luz Bejerano ID: 12-703-1665 Index 1. Introduction 2. Definition of the topic 3. Terms 4. Examples 5. Conclusion 6. Bibliography Introduction A study of the definite integral is presented, which is one of the important topics of differential and integral calculus. The definite integral is a topic of great importance, its applications have quite wide scopes, in branches and areas such as the industrial aspect, the resolution of problems raised, both in mathematics itself and in physics and some concepts of the same, be work, pressure, hydrostatic force, moments and centers of mass, among others. Definition of the topic The definite integral is one of the fundamental concepts of Mathematical Analysis The definite integral of f(x) on the interval [a,b] is equal to the limited area between the graph of f(x), the abscissa axis, and the vertical lines x = a and x = b (under the hypothesis that function f is positive). This integral is represented by: a is the lower limit of integration and b is the upper limit of integration. If the function F is a primitive function of f on the interval [a, b], by Barrow's Rule we have that: Terms The value of the definite integral changes sign if the limits of integration are swapped. If the limits of integration coincide, the definite integral is equal to zero. If c is an interior point of the interval [a, b], the definite integral decomposes as a sum of two integrals extended to the intervals [a, c] and [c, b]. The definite integral of a sum of functions is equal to the sum of integrals. The integral of the product of a constant times a function is equal to the constant times the integral of the function. Examples Conclusion It is shown that the calculation of an integral is a process by which the primitive of the function is obtained. They are the representation of the area covered by a function graphed on a Cartesian plane. This is a fundamental part in the calculation of surfaces, volumes and other measures that can be determined, and usually are, by a function. It is in this way that engineers manage to do complex calculations correctly and efficiently to build infrastructure and technology, much of which is used by a large part of today's population. Bibliographic reference https://xornalgalicia.com/localidades/15934-laimportancia-de-las-integrales-matematicas https://www.ecured.cu/Integral_definida
