integral from 0 to 1 of x*3x^2

Lösung

\int_{0}^{1} x \cdot 3 x^{2} d x

\frac{3}{4}

Dezimale

0.75

Schritte zur Lösung

\int_{0}^{1} x \cdot 3 x^{2} d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{1} x x^{2} d x

Vereinfache

x x^{2} : x^{3}

= 3 \cdot \int_{0}^{1} x^{3} d x

Wende die Potenzregel an

= 3 [\frac{x ^{4}}{4}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{4}

= 3 \cdot \frac{1}{4}

Vereinfache

= \frac{3}{4}

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