1. Finding constant of integration
Greg Kelly, Hanford High School, Richland, Washington

2. First, a little review:
Consider: or
then:
It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears.
However, when we try to reverse the operation:
Given:
find
We don’t know what the constant is, so we put “C” in the answer to remind us that there might have been a constant.

3. If we have some more information we can find C.
Given: and when , find the equation for .
This is called an initial value problem. We need the initial values to find the constant.
An equation containing a derivative is called a differential equation. It becomes an initial value problem when you are given the initial condition and asked to find the original equation.

4. Integrals such as are called definite integrals because we can find a definite value for the answer.
The constant always cancels when finding a definite integral, so we leave it out!

5. Integrals such as are called indefinite integrals because we can not find a definite value for the answer.
When finding indefinite integrals, we always include the “plus C”.