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/s^{2} or \(g\approx9.8\) m/s^{2} . 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:

7.2 Basic Integration Formulas

7.4 Integration by Substitution

7.5 Integrals of Trigonometric Functions