Proper integral is a kind of integral in Integral calculus, a branch of Mathematics in Calculus .

## Definition

A integral with finite value of Limit of a function and whose value does not approach to infinity. [1] [2] [3] [4] [5]

${\displaystyle \int Sin(x)/x\,dx}$ is finite and ${\displaystyle \lim _{x\to 0}Sin(x)/x=1}$

## Conditions

Every integral whose value is finite is not proper integral until the limit existence is ensured. [5]

Limit existence is possible when the limit at right and left neighborhood is equal to limit itself. This condition ensures the integral to be proper integral.

## Properties

It has Properties of addition and subtraction

1.Addition${\displaystyle \int (f(x)+g(x))\,dx=\int f(x)\,dx+\int g(x)\,dx}$

2. Subtraction${\displaystyle \int (f(x)-g(x))\,dx=\int f(x)\,dx-\int g(x)\,dx}$

## References

1. ^ Krishna's Series: Integral Calculus (Fully Solved); First Edition: 1987; Siventeenth Edition: 2008. Krishna Prakashan Media.
2. ^ Mittal, P. K. (March 2005). Integral Calculus. S. Chand Publishing. ISBN  978-81-219-0681-4.
3. ^ Society, American Mathematical (1901). Transactions of the American Mathematical Society. American Mathematical Society.
4. ^ Weisstein, Eric W. "Proper Integral". mathworld.wolfram.com. Retrieved 2022-08-29.
5. ^ a b "calculus - What is the condition that determines a proper integral?". Mathematics Stack Exchange. Retrieved 2022-08-29.