integral from 0 to 1 of pix^2

Lösung

\int_{0}^{1} π x^{2} d x

\frac{π}{3}

Dezimale

1.04719 \dots

Schritte zur Lösung

\int_{0}^{1} π 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}^{1} x^{2} d x

Wende die Potenzregel an

= π [\frac{x ^{3}}{3}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{3}

= π \frac{1}{3}

Vereinfache

= \frac{π}{3}

\int_{0}^{1} 2 x^{2} (x^{3} - 1)^{8} d x

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