Definition
Stem Function
Let
be an interval and a function. A function is called a stem function (or antiderivative) of if it is differentiable on and its derivative is equal to : The set of all stem functions of
is called the indefinite integral of , denoted by . If is a stem function of , then any other stem function differs from only by a constant : .
Properties
- Linearity: If
and are stem functions of and respectively, then is a stem function of . - Fundamental Theorem of Calculus: If
is continuous on and is a stem function of , then: - Existence: Every continuous function on an interval has a stem function.