이상적분,improper_integral

Difference between r1.1 and the current

@@ -8,35 +8,30 @@

극한값이 수렴converge하거나 발산diverge함.

mklink: 무한대 infinity

[[RR:이상적분improper_integral]]

Sub:
[[가우스_적분,Gaussian_integral]]
{
$\int_{-\infty}^\infty e^{-x^2}\,dx = \sqrt{\pi}$

[[가우스_함수,Gaussian_function]] $f(x)=e^{-x^2}$ 을 실직선(real line) 전체에 대해 적분한 것
{
일반적으로
$f(x)=ae^{-\frac{(x-b)^2}{2c^2}$
꼴의 함수. 가령
$\int_0^1\frac1{x^p}dx=\begin{cases}\end{cases}$
$\int_1^{\infty}\frac1{x^p}dx=\begin{cases}\text{diverges} &\text{if }p\le 1\\ \text{converges to }\frac{1}{p-1}&\text{if }p>1 \end{cases}$

Related: [[가우스_적분,Gaussian_integral]]
}
적분구간을 조절하면 [[오차함수,error_function]]와 관련.
[[정규분포,normal_distribution]]의 [[누적분포함수,cumulative_distribution_function,CDF]]와 관련.
Twins:
WpKo:가우스_적분
https://angeloyeo.github.io/2020/01/17/Gaussian_Integral.html
WpEn:Gaussian_integral
https://mathworld.wolfram.com/GaussianIntegral.html
}
----
Sites:
https://tutorial.math.lamar.edu/classes/calcii/improperintegrals.aspx
https://www.sfu.ca/math-coursenotes/Math%20158%20Course%20Notes/sec_ImproperIntegrals.html

Twins:
[[WpKo:이상_적분]]
[[WpEn:Improper_integral]]
[[WpKo:이상_적분]]
[[WpEn:Improper_integral]]
https://mathworld.wolfram.com/ImproperIntegral.html
https://encyclopediaofmath.org/wiki/Improper_integral
https://proofwiki.org/wiki/Definition:Improper_Integral
https://planetmath.org/ImproperIntegral
https://everything2.com/title/Improper+Integral (tmp)

Up: [[적분,integration]] > [[정적분,definite_integral]]
## mathworld에 의하면 정적분임.


AKA 특이적분

  • 유한한 닫힌 구간에서만 정의되는 함수가 아니라거나
  • 불연속인 함수라거나
또 있나?

적분 식 앞에 극한,limit을 붙여서 정의함.

극한값이 수렴converge하거나 발산diverge함.

mklink: 무한대 infinity