# 5 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 \(g\approx32\) 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 an unknown function whose
derivative is known. 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 \(f\).

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