integral from 0 to 1 of ax^2

Lösung

\int_{0}^{1} a x^{2} d x

\frac{a}{3}

Schritte zur Lösung

\int_{0}^{1} a x^{2} d x

Entferne die Konstante:

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

= a \cdot \int_{0}^{1} x^{2} d x

Wende die Potenzregel an

= a [\frac{x ^{3}}{3}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{3}

= a \frac{1}{3}

Vereinfache

= \frac{a}{3}

\int_{0}^{2} \frac{8 x}{2 x ^{2} + 1} d x

\int_{0}^{2} - 4 d x

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\int_{0}^{1} 5 x^{2} + x d x