7. Indefinite Integrals

In many problems, it is desired to reverse the process of differentiation. For example, we know from physics that the acceleration of a falling object, if the air resistance is negligible, is a constant $a(t)=-g$ where $g\approx 32$ ft/s² or $g\approx 9.8$ m/s² . So how can we use this to find the velocity and the position of the object? In this chapter, we study different techniques to find a function $F$ whose derivative is a given function $f$. If such a function $F$ exists, it is called an integral (or antiderivative) of $f$. Notice that if $F$ is an antiderivative of $f$, since the derivative of a constant is zero, $F(x)+C$ where $C$ is a constant is also an antiderivative of $f$.

In this chapter, we will learn:

7.1 Definition

7.2 Rules for Integrating Standard Elementary Forms

7.3 Constant of Integration

7.4 Integration by Substitution