integral from 0 to 1 of (x^2)/2

Lösung

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

\frac{1}{6}

Dezimale

0.16666 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Potenzregel an

= \frac{1}{2} [\frac{x ^{3}}{3}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{3}

= \frac{1}{2} \cdot \frac{1}{3}

Vereinfache

= \frac{1}{6}

\int_{- 3}^{1} \frac{1}{x ^{4}} d x

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