integral from 0 to infinity of 2/(3+x^2)

Lösung

\int_{0}^{\infty} \frac{2}{3 + x ^{2}} d x

\frac{π}{3}

Dezimale

1.81379 \dots

Schritte zur Lösung

\int_{0}^{\infty} \frac{2}{3 + x ^{2}} d x

Berechne das unbestimmte Integral:

\int \frac{2}{3 + x ^{2}} d x = \frac{2}{3} arctan (\frac{x}{3}) + C

Berechne die Grenzen:

\int_{0}^{\infty} \frac{2}{3 + x ^{2}} d x = \frac{π}{3} - 0

= \frac{π}{3} - 0

Vereinfache

= \frac{π}{3}

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