EXAMPLE AND COUNTEREXAMPLES IN DOUBLE INTEGRAL AND ITERATED INTEGRAL

Kim, Byung-Moo; Kim, Byung-Moo

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.2 No.2

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

1995, v.2 no.2, pp.127-132

Kim, Byung-Moo

Kim,, B. (1995). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 2(2), 127-132.

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Abstract

[1] Show that ∫<TEX>$\_$</TEX>0/<TEX>$\^$</TEX>1/ [∫<TEX>$\_$</TEX>0/<TEX>$\^$</TEX>1/ f(<TEX>$\chi$</TEX>,y)dy] d<TEX>$\chi$</TEX> = ∫<TEX>$\_$</TEX>0/<TEX>$\^$</TEX>1/[∫<TEX>$\_$</TEX>0/<TEX>$\^$</TEX>1/ f(<TEX>$\chi$</TEX>,y)d<TEX>$\chi$</TEX>] Counterexample: If pk denotes the k-th prime number, let S(pk) = (equation omitted), let S = ∪<TEX>$\_$</TEX>k=1/<TEX>$\^$</TEX><TEX>$\infty$</TEX>/ S(pk), and let Q = [0, 1]<TEX>${\times}$</TEX>[0, 1]. Define f on Q as follows; f(<TEX>$\chi$</TEX>, y) = 0 (<TEX>$\chi$</TEX>, y)<TEX>$\in$</TEX>S, f(<TEX>$\chi$</TEX>, y) = 1 (<TEX>$\chi$</TEX>, y)<TEX>$\in$</TEX>Q - S.(omitted)

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Vol.2 No.2

Abstract

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics