Short and Sweet Calculus

# 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/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 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 $$f$$.