Uegentlig integral av x

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4 years, 1 month ago

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Fra kalkulus 1 vet vi at $\int\limits_{-b}^bx\mathrm dx=\frac{x^2}{2}\Big|_{-b}^b=\frac{b^2}{2}-\frac{(-b)^2}{2}=0$

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Hva kan man si om uegentlige integralet $\int\limits_{-\infty}^{\infty}x\mathrm dx$ ?

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Integralet $\int\limits_{-\infty}^{\infty}x\mathrm dx$ er likt et endelig tall men ikke 0

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Integralet $\int\limits_{-\infty}^{\infty}x\mathrm dx$ er likt 0

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Integralet $\int\limits_{-\infty}^{\infty}x\mathrm dx$ divergerer

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Integralet $\int\limits_{-\infty}^{\infty}x\mathrm dx$ eksisterer ikke fordi integralet $\int\limits_{0}^{\infty}x\mathrm dx$ divergerer

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This question is used in the following exams:

Uke 11 by Elena Malyutina in Elena's workspace.
Uegentlige integraler by Elena Malyutina in Elena's workspace.
Rekker og Uegentlige integraler (uke 6) by Glen Wilson in Glen's workspace.

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Elena Malyutina 4 years, 1 month ago

Elena Malyutina 4 years, 1 month ago

Elena Malyutina 4 years, 1 month ago

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