7.8 - 7.8 Improper Integrals 1 Quote You and I are...

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7.8 Improper Integrals1.Quote.You and I are essentially infinite choice-makers.In everymoment of our existence, we are in that field of all possibilities wherewe have access to an infinity of choices.(Deepak Chopra, Indian ayurvedic Physician and Author, 1947-)2.Problem.Evaluate the area of the region bounded by the curvesy=1x2, y= 0, x= 1.3.Improper Integral of Type I.(a)IfRtaf(x)dxexists for every numberta, thenZaf(x)dx= limt→∞Ztaf(x)dxprovided hat this limit exists (as a finite number).(b)IfRbtf(x)dxexists for every numbertb, thenZb-∞f(x)dx=limt→-∞Zbtf(x)dxprovided hat this limit exists (as a finite number).The improper integralsRaf(x)dxandRb-∞f(x)dxare calledcon-vergentif the corresponding limit exists anddivergentif thelimit does not exists.1

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