The motivation of integration.
Welcome to the new, fantastic and marvelous field of integration.! In this section, you will be able to learn about how to use integration to solve problems in our lives.
Firstly, let’s move on to the history of the development of this mathematical concept. Over 2000 years ago, the way to calculate surface area and volume was found by a mathematician Archimedes. However, the method Archimedes found was not impeccable. For example, this algorithm can only solve simple geometric solids’ areas or volumes, such as a sphere, instead of irregular patterns, such as arches. In the 1600s, Gottfried Wilhelm Leibniz and Isaac Newton found calculus in which the fundamental idea was differentiation and integration could undo each other. This mathematical concept solves many problems in mathematics, astronomy, and physics. In 1700s-1900s, the development of integration was fast. Joseph Fourier, one of the great mathematician，found series about integration which can be used in many fields nowadays. Moreover, after Carl Friedrich Gauss, known as the Prince of Mathematics, first drawn the table of integration, then more people noticed the importance of integration and got interested in this concept. Many mathematicians such as Cauchy, Riemann and Lebesgue made a lot of contributions in developing integration. Finally, integration was published on Mathematica in 1988 and accepted widely. Obviously, integration is not only a mathematical concept but also a great treasure of human history. After learning about the history of integration, let’s move on to its practicability. Integration was applied in many fields of our life besides math. In the area of the economy, integration can be used to calculate many problems such as the best profit and the lowest cost. After that, people can find the most efficient ways of production and management that can improve the development of economy all over the world. In physics, integration is used to solve both common questions such as velocity and complex problems such as the distance between two planets. The application of integration in physics field can help people explore the unknown phenomenon. For example, the gravity was found by many calculations by scientists. Moreover, most of the concepts in physics can be inferred by using integration and differentiation such as the transformation between acceleration and velocity. In the future, some of us might be able to discover the truth of universe by using integration. In chemistry engineering, integration is used to determine the electrons and reactions, which is related to kinds of materials in our life. Frequently, integration is used in many of field observations. Researchers like to apply integration when calculating the data of regions, such as their areas and volumes.
Therefore, integration plays an important role all over the world. We are strongly encouraged to learn about this concept and apply it in kinds of fields of our lives.