# Integral 0 To Infinity – Integral Calculator: Integrate With Wolfram

An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration. Improper integrals cannot be computed using a normal Riemann integral.

Đang xem: Integral 0 to infinity

For example, the integral

is an improper integral. Some such integrals can sometimes be computed by replacing infinite limits with finite values

and then taking the limit as

infty” />,

infty)int_1^yx^(-2)dx” />

infty)1-1/y” />

with one infinite limit and the other nonzero may also be expressed as finite integrals over transformed functions. If

decreases at least as fast as

, then let

REFERENCES:

Jeffreys, H. and Jeffreys, B.S. “Infinite and Improper Integrals.” §1.104 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp.33-34, 1988.

Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; and Vetterling, W.T. “Improper Integrals.” §4.4 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp.135-140, 1992.

CITE THIS AS:

Weisstein, Eric W. “Improper Integral.”From wnyrails.org–A wnyrails.org Web Resource. https://wnyrails.org/ImproperIntegral.html

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