integral from 0 to 2 of z^2ln(z)

Lösung

\int_{0}^{2} z^{2} ln (z) d z

\frac{8}{3} ln (2) - \frac{8}{9}

Dezimale

0.95950 \dots

Schritte zur Lösung

\int_{0}^{2} z^{2} ln (z) d z

Wende die partielle Integration an

= [\frac{1}{3} z^{3} ln (z) - \int \frac{z ^{2}}{3} d z]_{0}^{2}

\int \frac{z ^{2}}{3} d z = \frac{z ^{3}}{9}

= [\frac{1}{3} z^{3} ln (z) - \frac{z ^{3}}{9}]_{0}^{2}

Berechne die Grenzen:

\frac{8}{3} ln (2) - \frac{8}{9}

= \frac{8}{3} ln (2) - \frac{8}{9}