Proper integral
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]
[math]\displaystyle{ \int Sin (x)/x \,dx }[/math] is finite and [math]\displaystyle{ \lim _{x \to 0} Sin (x)/x = 1 }[/math]
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[math]\displaystyle{ \int (f(x)+g(x))\,dx =\int f(x)\,dx + \int g(x)\,dx }[/math]
2. Subtraction[math]\displaystyle{ \int (f(x)-g(x))\,dx=\int f(x)\,dx-\int g(x)\,dx }[/math]
References
- ↑ (in en) Krishna's Series: Integral Calculus (Fully Solved); First Edition: 1987; Siventeenth Edition: 2008. Krishna Prakashan Media. https://books.google.com/books?id=wyIoOiBhPsAC&dq=Proper+Integral&pg=RA1-PA322.
- ↑ Mittal, P. K. (March 2005) (in en). Integral Calculus. S. Chand Publishing. ISBN 978-81-219-0681-4. https://books.google.com/books?id=bLlGhMaSoBgC&dq=Proper+Integral&pg=PA468.
- ↑ Society, American Mathematical (1901) (in en). Transactions of the American Mathematical Society. American Mathematical Society.. https://books.google.com/books?id=apgLAAAAYAAJ&dq=Proper+Integral&pg=PA465.
- ↑ Weisstein, Eric W.. "Proper Integral" (in en). https://mathworld.wolfram.com/.
- ↑ 5.0 5.1 "calculus - What is the condition that determines a proper integral?" (in en). https://math.stackexchange.com/questions/1935337/what-is-the-condition-that-determines-a-proper-integral.
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