In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number, ∞, -∞, or in some instances as both endpoints approach limits. Such an integral is often written symbolically just like a standard definite integral, in some cases with infinity as a limit of integration. Specifically, an improper integral is a limit of the form: limb→∞∫ₐᵇf(x) dx, limₐ→₋∞∫ₐᵇf(x) dx, or limc→b⁻∫ₐᶜf(x) dx, limc→ₐ⁺∫cᵇf(x) dx, in which one takes a limit in one or the other (or sometimes both) endpoints (Apostol 1967, §10.23).

IMPROPER INTEGRALS +3 more

by VEDANT MILIND ATHAVALE

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