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 $$g\approx32$$ ft/s2 or $$g\approx9.8$$ 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 Basic Integration Formulas

7.3 Constant of Integration

7.4 Integration by Substitution