## Mathematical Analysis## Integral Calculus |

## What is the definite integral? |

In actuality, the area shown on page 233 is actually determined using limits. In the function *f(x)*, as *n* gets larger, the numbers determined by left *(n)* and right *(n)* will get closer and closer to the area Ω. This is seen as the following notation:

Thus, in the calculus terms, the area of the above graphic region is called the definite integral (also said as “the integral”) of *f(x)* from *a* to *b*, and is denoted by the following notation:

The variable *x* can be replaced with any other variable. In other words, if the limits of integration *(a* and *b)* are specified, it is called a definite integral, and it can be interpreted as an area or a generalization of an area.