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- Jan 26, 2012

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Thanks to those who participated in last week's POTW!! Here's this week's problem.

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\[\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2}e^{-(x^2+y^2+z^2)}\,dx\,dy\,dz = 2\pi\]

(Note that the improper triple integral is defined as the limit of a triple integral over a solid sphere as the radius of the sphere increases indefinitely.)

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Here's a hint for this week's problem.

Remember to read the POTW submission guidelines to find out how to submit your answers!

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**Problem**: Show that\[\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^2+y^2+z^2}e^{-(x^2+y^2+z^2)}\,dx\,dy\,dz = 2\pi\]

(Note that the improper triple integral is defined as the limit of a triple integral over a solid sphere as the radius of the sphere increases indefinitely.)

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Here's a hint for this week's problem.

Use spherical coordinates.

Remember to read the POTW submission guidelines to find out how to submit your answers!

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