integral from 0 to infinity of e^{-r^2}r

Lösung

\int_{0}^{\infty} e^{- r^{2}} r d r

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

\int_{0}^{\infty} e^{- r^{2}} r d r

Berechne das unbestimmte Integral:

\int e^{- r^{2}} r d r = - \frac{1}{2} e^{- r^{2}} + C

Berechne die Grenzen:

\int_{0}^{\infty} e^{- r^{2}} r d r = 0 - (- \frac{1}{2})

= 0 - (- \frac{1}{2})

Vereinfache

= \frac{1}{2}

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