The Common Techniques and Applications in Calculus

Calculus is a pivotal subject in advanced mathematics since it is indispensable in various areas nowadays. It has many applications in other subjects like physics engineering and social science. However, compared with elementary mathematics, calculus is not easy to learn and integral is not easy to calculate because it is usually challenging to find out the antiderivative or the integral does not have a closed form. Thus, it is necessary to learn at least the basic techniques in calculus, which can help simplify the difficulty to solve the integrals in some extent. In this paper, the author will introduce three common techniques that everyone who learns calculus may use. These techniques are substitution, partial fraction, and integration by part, and illustrate their applications on several representative examples. In doing so, this can help readers grasp the most fundamental techniques in calculus, which is beneficial for them to further learn the calculus and apply them skillfully to calculate various integrals.