The Indefinite Integral and the Definite Integral

Integration I

In this course, Professor Ivan Contreras (Amherst College) gives an introduction to integration. In the first mini-lecture, we learn about the indefinite integral and the definite integral, and think about how they can be used to calculate antiderivatives and areas under curves. In the second mini-lecture, we introduce the fundamental theorem of calculus. In the third mini-lecture, we learn about the power rule, addition rule, subtraction rule, and constant rule for integration. In the fourth mini-lecture, we discuss how to integrate exponential functions, reciprocal functions, and trigonometric functions. In the fifth mini-lecture, we learn how to construct integrals that describe the area between two curves.

The Indefinite Integral and the Definite Integral

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.