The Indefinite Integral and the Definite Integral

About the lecture

In this mini-lecture, we learn about the indefinite integral and the definite integral. In particular, we think about: (i) the use of calculus in scientific breakthroughs and applications; (ii) the derivative as the instantaneous rate of change; (ii) the integral, sometimes called the antiderivative, as the area under a curve; (iii) how to find the antiderivative F(x) of a function f(x), where F’(x) = f(x); (iv) the indefinite integral, which is a function and serves as an alternative way of representing F(x) in terms of f(x); (v) the definite integral, which is a number given by the indefinite integral and a set of bounds; and (vi) exercises for students to try on their own with solutions included at the end.

About the lecturer

Ivan Contreras is an Assistant Professor of Mathematics at Amherst College in Massachusetts. His research lies at the intersection of geometry, topology, and mathematical physics. In particular, he focuses on connecting classical and quantum understandings of physical systems by using the tools of differential geometry like Lie groups, Lie algebras, and Poisson structures. Professor Contreras enjoys teaching a wide range of topics at various levels, including introductory calculus, linear algebra, Lie groups and Lie algebra, and differential geometry.