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9.3.E: Problemas en Integrales de Cauchy
https://espanol.libretexts.org/Matematicas/Analisis/Libro%3A_An%C3%A1lisis_matem%C3%A1tico_(Zakon)/09%3A_C%C3%A1lculo_usando_la_teor%C3%ADa_de_Lebesgue/9.03%3A_Integrales_inadecuadas_(Cauchy)/9.3.E%3A_Problemas_en_Integrales_de_Cauchy
(i) $\int_{1}^{\infty} \int_{1}^{\infty} e^{-x y} d y d x=\int_{1}^{\infty} \frac{1}{x} e^{-x} d x \leq \frac{1}{e}(\text { converges, by } 3(\mathrm{i}))$ . ii)\(\int_{0}^{\infty} \int_{0}^{\infty} e...(i) $\int_{1}^{\infty} \int_{1}^{\infty} e^{-x y} d y d x=\int_{1}^{\infty} \frac{1}{x} e^{-x} d x \leq \frac{1}{e}(\text { converges, by } 3(\mathrm{i}))$ . ii) $\int_{0}^{\infty} \int_{0}^{\infty} e^{-x y} d y d x \geq \int_{1}^{\infty} \int_{0}^{\infty} e^{-x y} d y d x=\int_{1}^{\infty} \frac{1}{x}\left(1-e^{-x}\right) d x \geq \int_{1}^{\infty}\left(\frac{1}{x}-e^{-x}\right) d x=\infty$ .

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