Applications of Antiderivatives
Sometimes, an antidifferentiation problem will also have an attached initial condition. This condition will allow us to obtain a definite integral in which we have solved for C. Consider the following example:
EXAMPLE 1
A common antidifferentiation application is a motion problem. An equation involving a derivative is called a differential equation. In motion problems, the velocity equation is our differential equation and can be integrated to find the motion equation. Similarly, an acceleration equation can be integrated to find a velocity equation. Initial conditions also play a role in these situations. Consider the following examples.
EXAMPLE 2
EXAMPLE 3
