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
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