integral from 1 to e of piln^2(y)

Lösung

\int_{1}^{e} π ln^{2} (y) d y

π (e - 2)

Dezimale

2.25654 \dots

Schritte zur Lösung

\int_{1}^{e} π ln^{2} (y) d y

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{1}^{e} ln^{2} (y) d y

Wende die partielle Integration an

= π [y ln^{2} (y) - \int 2 ln (y) d y]_{1}^{e}

\int 2 ln (y) d y = 2 (y ln (y) - y)

= π [y ln^{2} (y) - 2 (y ln (y) - y)]_{1}^{e}

Berechne die Grenzen:

e - 2

= π (e - 2)

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