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

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

Example: ∫ *e* −*t**dt*

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:

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: ∞∫0*e* −*t**dt*

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

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12th Business Maths and Statistics : Chapter 2 : Integral Calculus - I : Gamma Integral | Exercise and Example Solved Problems with Answer, Solution

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