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Beliebt Rechnen >

integral from-infinity to 0 of 1/(x^2+1)

Lösung

\int_{- \infty}^{0} \frac{1}{x ^{2} + 1} d x

Lösung

\frac{π}{2}

+1

Dezimale

1.57079 \dots

Schritte zur Lösung

\int_{- \infty}^{0} \frac{1}{x ^{2} + 1} d x

Berechne das unbestimmte Integral:

\int \frac{1}{x ^{2} + 1} d x = arctan (x) + C

Berechne die Grenzen:

\int_{- \infty}^{0} \frac{1}{x ^{2} + 1} d x = 0 - (- \frac{π}{2})

= 0 - (- \frac{π}{2})

Vereinfache

= \frac{π}{2}

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