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# Gamma Integral

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

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 [ab].

Example: ## Improper definite integral:

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

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    