Concept of an elementary work as introduction to the line integral in engineering studies

The paper is devoted to the line integral topic belonging to the section of vector calculus in Mathematical Analysis applied to the undergraduate Mechanical Engineering program. An efficient way of teaching line integrals is proposed and developed based on the elementary work/force principles. By this way, the mathematical concept of the line integral is supposed to be learned in harmony with the elementary mechanics to appreciate its diversity and to set up the right idea about the scientific area covered by Mechanical Engineering and related academic and technical fields. In terms of practical training, the research also offers two new techniques of analytical calculus for line integrals containing singularities and provides a new coherent engineering approach to deal with vector fields as integrands in line integrals.