integral from 0 to L of (L-x)^2

Lösung

\int_{0}^{L} (L - x)^{2} d x

\frac{L ^{3}}{3}

Schritte zur Lösung

\int_{0}^{L} (L - x)^{2} d x

Wende U-Substitution an

= \int_{L}^{0} - u^{2} d u

Entferne die Konstante:

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

= - \int_{L}^{0} u^{2} d u

Wende die Potenzregel an

= - [\frac{u ^{3}}{3}]_{L}^{0}

Berechne die Grenzen:

- \frac{L ^{3}}{3}

= - (- \frac{L ^{3}}{3})

Vereinfache

= \frac{L ^{3}}{3}

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