09hw10 - f is Riemann integrable on each interval [0 ,b ]....

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Mathematics 241, Problem Set #10, due November 4, 2009 Write clear proofs that have good grammar and consist of complete sentences. Royden, page 291, #1. Royden, page 298, #3, 4. Royden, page 310, #21,24,25,29. 8. (a) Let f ( x ) = x - 1 sin x for x > 0 and f (0) = 1. Explain why
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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 x-1 sin xdx = 2 by considering the double integral Z Z b e-xy sin xdxdy....
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This note was uploaded on 11/18/2009 for the course MATH 241 taught by Professor Reed during the Spring '09 term at Duke.

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