## Mathematical Analysis## Integral Calculus |

## What are some properties of the definite integral? |

There are several useful properties of the definite integral. *Theorem one* is based on the idea that if f(x) and *g(x)* are defined and continuous on [*a*, *b*], except perhaps at a finite number of points, then the following applies in which alpha is a constant:

*Theorem two* is based on the idea that if *f*(x) is defined and continuous on [*a*, *b*], except at a finite number of points, then the following applies for any arbitrary numbers *a* and *b*, and any *c* ∈ [*a*, *b*]: