Unformatted text preview: f is Riemann integrable on each interval [0 ,b ]. Prove that R ∞  f ( x )  dx = ∞ (Lebesgue integral). (b) Prove that lim b →∞ R b x1 sin xdx = π 2 by considering the double integral Z ∞ Z b exy sin xdxdy....
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 Spring '09
 Reed
 Math, Riemann, integral e−xy sin

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