Question

40. \( \star \) Evalúe \[ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^{2}+y^{2}+z^{2}} e^{-x^{2}-y^{2}-z^{2}} d z d y d x \]

          40. \( \star \) Evalúe
\[
\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^{2}+y^{2}+z^{2}} e^{-x^{2}-y^{2}-z^{2}} d z d y d x
\]

40. ⋆ Evalúe

∫-∞^∞∫-∞^∞∫-∞^∞√(x^2+y^2+z^2) e^-x^2-y^2-z^2 d z d y d x

Added by Aitor S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 15

Instant Answer

Solved by Expert Carson Merrill

Step 1

The given integral is: \[ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^{2}+y^{2}+z^{2}} e^{-x^{2}-y^{2}-z^{2}} \, dz \, dy \, dx \] Show more…

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40. \( \star \) Evalúe \[ \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \sqrt{x^{2}+y^{2}+z^{2}} e^{-x^{2}-y^{2}-z^{2}} d z d y d x \]