Lecture 18 : Improper integrals - IIT Kanpur

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1Lecture 18 : Improper integralsWe defined baf(t)dtunder the conditions thatfis defined and bounded on the bounded interval[a, b]. In this Lecture , we will extend the theory of integration to bounded functions defined onunbounded intervals and also to unbounded functions defined on bounded or unbounded integral of the first kind:Supposefis (Riemann) integrable on [a, x] for allx > a, , xaf(t)dtexists for allx > a. If limx xaf(t)dt=Lfor someL R,then we say thatthe Improper integral (of the first kind) af(t)dtconverges toLand we write af(t)dt= , we say that the Improper integral af(t) that the definition of convergence of Improper integrals is similar to the one given forseries.

1 Lecture 18 : Improper integrals We deflned Rb a f(t)dt under the conditions that f is deflned and bounded on the bounded interval [a;b].In this lecture, we will extend the theory of integration to bounded functions deflned on unbounded intervals and also to unbounded functions deflned on bounded or unbounded intervals.

  Lecture, Relating, Improper, Improper integrals, Lecture 18