ANTIDERIVATIVES

1. Definition
   Suppose that F'(x) = f(x).  Then F(x) is called an antiderivative of f(x). 

2.  Examples

   1. An antidervative of sin(x) is -cos(x).

   2. An antiderivative of x² is 1/3 x³

   We will do several others in class as exercises.

3. Differential Equations  
   Suppose we want to find the solution to
   dy/dx = f(x)
   This is another way of asking for the antiderivative of f.  Several examples will be given.

4. Notation
   The antiderivative of f(x) will be denoted by
   
   

\