integral from 0 to 9 of pi(2sqrt(x))^2

Lösung

\int_{0}^{9} π (2 x)^{2} d x

π 162

Dezimale

508.93800 \dots

Schritte zur Lösung

\int_{0}^{9} π (2 x)^{2} d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{9} (2 x)^{2} d x

Wende die partielle Integration an

= π [4 x^{2} - \int 4 x d x]_{0}^{9}

\int 4 x d x = 2 x^{2}

= π [4 x^{2} - 2 x^{2}]_{0}^{9}

Vereinfache

= π [2 x^{2}]_{0}^{9}

Berechne die Grenzen:

162

= π 162

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