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Beliebt Rechnen >

integral from-infinity to 0 of z/(z^4+9)

Lösung

\int_{- \infty}^{0} \frac{z}{z ^{4} + 9} d z

Lösung

- \frac{π}{12}

+1

Dezimale

- 0.26179 \dots

Schritte zur Lösung

\int_{- \infty}^{0} \frac{z}{z ^{4} + 9} d z

Berechne das unbestimmte Integral:

\int \frac{z}{z ^{4} + 9} d z = \frac{1}{6} arctan (\frac{z ^{2}}{3}) + C

Berechne die Grenzen:

\int_{- \infty}^{0} \frac{z}{z ^{4} + 9} d z = 0 - \frac{π}{12}

= 0 - \frac{π}{12}

Vereinfache

= - \frac{π}{12}

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