Integral Calculus: An Introduction to the Anti-Derivative 

About the Class

If a function has an integral, it is said to be integrable. The function for which the integral is calculated is called the integrand. The region over which a function is being integrated is called the domain of integration.

In this class, the presenter will introduce the concept of Integration. We will describe it as simply, the reverse process of differentiation, hence, also called Anti-Differentiation.

The integral may be found without a definite specification or for a particular region leading to the development of indefinite & definite integrals. In case of the definite integrals, the domain of integration is defined by specifying the upper & lower limits of the enclosed region. Also, definite integrals may not be referred to as anti-derivatives which is a term used only for indefinite integrals in accordance with the fundamental theorem of calculus. Besides, the indefinite integral may be a constant or a function of the independent variable however, the definite integral is always constant.

We will also discuss about the geometrical & physical representation & significance of the integral. When we look into the practical applications of integrals, they appear in a number of practical situations.

Consider a swimming pool. If it is rectangular, then from its length, width, and depth we can easily determine the volume of water it can contain (to fill it), the area of its surface (to cover it), and the length of its edge (to rope it). But if it is oval with a rounded bottom, all of these quantities call for integrals. The best of problems in Physics too involve the integral.

Language of instruction:

Keywords: integration, calculus, integrand, domain of integration, anti-differentiation, indefinite integrals, definite integrals