integral from-infinity to infinity of e^{-4x^2}

Lösung

\int_{- \infty}^{\infty} e^{- 4 x^{2}} d x

\frac{π}{2}

Dezimale

0.88622 \dots

Schritte zur Lösung

\int_{- \infty}^{\infty} e^{- 4 x^{2}} d x

Berechne das unbestimmte Integral:

\int e^{- 4 x^{2}} d x = \frac{π}{4} erf (4 x) + C

Berechne die Grenzen:

\int_{- \infty}^{\infty} e^{- 4 x^{2}} d x = \frac{π}{4} - (- \frac{π}{4})

= \frac{π}{4} - (- \frac{π}{4})

Vereinfache

= \frac{π}{2}

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