Gamma Integral

Gamma Integral

Gamma integral is an important result which is very useful in the evaluation of a particular type of an improper definite integrals.

First, let us know about the concepts of indefinite integrals, proper definite integrals and improper definite integrals

Indefinite integral:

An integral function which is expressed without limits, and so containing an arbitrary constant is called an indefinite integral

Example:    ∫ e −tdt

Proper definite integral:

Proper definite integral is an integral function, which has both the limits a and b are finite and the integrand f(x) is continuous in [a, b].

Example:   

Improper definite integral:

An improper definite integral is an integral function, in which the limits either a or b or both are infinite, or the integrand f(x) becomes infinite at some points of the interval [a, b].

Example:    ∞∫0e −tdt

Properties:

1.┌ (n) = (n − 1)G(n − 1), n > 1

2.┌ (n + 1) = n┌ (n ), n > 0

3.┌(n + 1) = n! , n is a positive integer.

4.┌ (1/2 ) = p

Example 2.80

Exercise 2.10

1. Evaluate the following

Answers: