integral from-2 to 1 of x(x-1)(x+2)

Lösung

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

\frac{9}{4}

Dezimale

2.25

Schritte zur Lösung

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

Wende die partielle Integration an

= [\frac{1}{6} (2 x^{4} + x^{3} - 6 x^{2} - 6 \cdot \int \frac{x ^{3}}{3} - \frac{x ^{2}}{2} d x)]_{- 2}^{1}

\int \frac{x ^{3}}{3} - \frac{x ^{2}}{2} d x = \frac{x ^{4}}{12} - \frac{x ^{3}}{6}

= [\frac{1}{6} (2 x^{4} + x^{3} - 6 x^{2} - 6 (\frac{x ^{4}}{12} - \frac{x ^{3}}{6}))]_{- 2}^{1}

Vereinfache

[\frac{1}{6} (2 x^{4} + x^{3} - 6 x^{2} - 6 (\frac{x ^{4}}{12} - \frac{x ^{3}}{6}))]_{- 2}^{1} : [\frac{1}{12} (3 x^{4} + 4 x^{3} - 12 x^{2})]_{- 2}^{1}

= [\frac{1}{12} (3 x^{4} + 4 x^{3} - 12 x^{2})]_{- 2}^{1}

Berechne die Grenzen:

\frac{9}{4}

= \frac{9}{4}

\int_{2}^{2} 1 + x^{3} d x

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