integral from 0 to x of 0.5x

Lösung

\int_{0}^{x} 0.5 x d x

0.25 x^{2}

Schritte zur Lösung

\int_{0}^{x} 0.5 x d x

Entferne die Konstante:

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

= 0.5 \cdot \int_{0}^{x} x d x

Wende die Potenzregel an

= 0.5 [\frac{x ^{2}}{2}]_{0}^{x}

Vereinfache

= 0.5 [0.5 x^{2}]_{0}^{x}

Berechne die Grenzen:

0.5 x^{2}

= 0.5 \cdot 0.5 x^{2}

Vereinfache

= 0.25 x^{2}

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