Show that for every parameter > 0 > 0 the function x ( sin

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Show that for every parameter α>0 the function

x(sinxx)3eαx

is integrable over (0,) and that the integral is continuous as a function of the parameter. [ find piecewise integrable majorants like in Problem 12.18 ; use the continuity lemma.]

Data from problem 12.8

Let A denote Lebesgue measure on R". (i) Let u L (A) and KCR" be a compact (i.e. closed and bounded) set.

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