 # how could we put the limits in definite integration 13 years ago

Hi,

Let me explain the concept of limits in Definite Integrals by taking a general example :

The following problems involve the limit definition of the definite integral of a continuous function of one variable on a closed, bounded interval. Begin with a continuous function on the interval . Let ... be an arbitrary (randomly selected) partition of the interval , which divides the interval into subintervals (subdivisions). Let ... be the sampling numbers (or sampling points) selected from the subintervals. That is, is in , is in , is in , ... , is in , is in ,

and is in .

Define the mesh of the partition to be the length of the largest subinterval. That is, let for and define .

The definite integral of on the interval is most generally defined to be .

For convenience of computation, a special case of the above definition uses subintervals of equal length and sampling points chosen to be the right-hand endpoints of the subintervals. Thus, each subinterval has length

equation (*) for and the right-hand endpoint formula is

equation (**) for . The definite integral of on the interval can now be alternatively defined by .

We will need the following well-known summation rules in case od different types of functions :

1. (n times) , where is a constant
2. 3. 4. 5. , where is a constant
6. Be sure to ask if anything's not clear.

Regards and Best of Luck,

Rajat