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Improper integral - Infinite bounds of integration | | Improper integral - Infinite bounds of integration: Encyclopedia II - Improper integral - Infinite bounds of integration | | The most basic of improper integrals are integrals such as:
As stated above, this need not be defined as an improper integral, since it can be construed as a Lebesgue integral instead. Nonetheless, for purposes of actually computing this integral, it is more convenient to treat it as an improper integral, i.e., to evaluate it when the upper bound of integration is finite and then take the limit as that bound approaches ∞. The antiderivative of the function being inte ...
See also:Improper integral, Improper integral - Infinite bounds of integration, Improper integral - Vertical asymptotes at bounds of integration, Improper integral - Cauchy principal values | | | Improper integral, Improper integral - Cauchy principal values, Improper integral - Infinite bounds of integration, Improper integral - Vertical asymptotes at bounds of integration | | |
| | | Improper integral: Encyclopedia II - Improper integral - Infinite bounds of integration
Improper integral - Infinite bounds of integration
The most basic of improper integrals are integrals such as:
As stated above, this need not be defined as an improper integral, since it can be construed as a Lebesgue integral instead. Nonetheless, for purposes of actually computing this integral, it is more convenient to treat it as an improper integral, i.e., to evaluate it when the upper bound of integration is finite and then take the limit as that bound approaches ∞. The antiderivative of the function being integrated is arctan x. The integral is
Other related archivesCauchy principal values, Chain rule, Continuity, Fourier transform, Function, Fundamental theorem, Implicit differentiation, Integration by cylindrical shells, Integration by disks, Integration by parts, Integration by substitution, Integration by trigonometric substitution, Lebesgue integral, Limits of functions, Lists of integrals, Mean value theorem, Product rule, Quotient rule, Related rates, Riemann integral, Taylor's theorem, Tensor calculus, Vector calculus, absolute values, antiderivative, antiderivatives, arctan, asymptote, calculus, definite integral, extended real number line, indeterminate form, integrals, limit, limits, mathematical analysis, pathologies, real number, vertical asymptote
 Adapted from the Wikipedia article "Infinite bounds of integration", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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