Definition of the definite integral and its meanings

In the general case the function may have negative values as well as positive ones. And partition the interval into subintervals by choosing arbitrary points may satisfy only the condition

.

We also can choose in an arbitrary manner the arbitrary points in each subinterval. In this case the sum is called the integral sum of the function on the interval.

Definition 9.1: The definite integral is the limit of the integral sum when the length of the greatest subinterval tends to zero.

, where .

The interval we call the interval of integration. The number is called the lower limit of integration and - the upper limit of integration.

Geometric meaning of the definite integral is the area under the curve from to .

Let us consider economical meaning of the definite integral by such example. Denote productivity of the labor of the worker at the time, then will be the number of the products produced by the workers during the time. In this example the definite integral is the number of the products produced by the worker during the time

Дата добавления: 2014-01-11