Comprehensive calculation with applications

Both at the level of mathematics and in the other areas of Basic Sciences and engineering, integral calculus plays a fundamental role, not only because of the variety of topics that its study contains, but also because of its applicability in solving various problems, such as the calculation of the area under a curve, the volume of a solid of revolution, the center of mass and gravity of an object, the moment of inertia and the arc length, among others. Starting from this perspective and the reality evidenced through experience, which teaches us that the use and application of integral calculus by university students is highly difficult, it is intended that they enhance their abilities to the approach, analysis, modeling and solution of problems present either in the framework of the study of the subjects of their study plan or in the context of applications such as research projects on topics of their specific knowledge and their future field of professional performance. To do this, this research product book has been designed, which makes available to the student –or researcher– a tool that initially allows them to appropriate the basic and fundamental concepts of integral calculus: antiderivative, definite integral, second fundamental theorem of calculus , area, volumes, etc. In this sense, the work - in addition to serving as a tool for students and / or researchers to appropriate specific content - will serve to stimulate the teaching-learning process of integral calculus, thereby seeking to contribute to the reduction of Failure and dropout rates for students in the Basic Sciences and Engineering programs of the Universidad del Atlántico.