Indefinite Integrals and Antiderivatives
As you remember from the atoms on antiderivatives,
For example, the function
![](../../../../../../../figures.boundless-cdn.com/17867/large/slope-field.jpg)
Slope Field
The slope field of
Indefinite integrals exhibit the following basic properties.
The Constant Rule for Indefinite Integrals$\int cf(x)dx = c\int f(x)dx$
The Sum Rule for Indefinite Integrals
The Difference Rule for Indefinite Integrals
Definite Integrals and the Net Change Theorem
Integrating over a specified domain yields what is called a "definite integral" (in that the domain is defined). Integrating over a domain
Such a problem can be solved using the net change theorem, which states that the integral of a rate of change is the net change (displacement for position functions):
Basically, the theorem states that the integral of or