integral from-1 to 2 of x((x^2)/3)

Lösung

\int_{- 1}^{2} x (\frac{x ^{2}}{3}) d x

\frac{5}{4}

Dezimale

1.25

Schritte zur Lösung

\int_{- 1}^{2} x \frac{x ^{2}}{3} d x

Entferne die Konstante:

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

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

Vereinfache

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

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

Wende die Potenzregel an

= \frac{1}{3} [\frac{x ^{4}}{4}]_{- 1}^{2}

Berechne die Grenzen:

\frac{15}{4}

= \frac{1}{3} \cdot \frac{15}{4}

Vereinfache

= \frac{5}{4}

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