Transcription of Lecture 18 : Improper integrals - IIT Kanpur
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Lecture 18 : Improper integrals - IIT Kanpur
1 Lecture 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.
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