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Mathematics-Online lexicon:

Inproper Integral

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For a function $ f$ , which is piecewise continuous on $ [a,b)$ , the concept of the integral is expandend by

$\displaystyle \int_a^b f = \lim_{c\to b-} \int_a^c f $

onto infinite intervals ($ b=\infty$ ) and onto unbounded integrands ( $ f(b)=\pm\infty$ ).

Analogous a singularity is been treated at the lower or at both limits. In the last case the limit has to be independent from the choice of the sequence $ c\to a+$ , $ d\to b-$ .

Examples:

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  automatically generated 9/12/2008