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

Lösung

\int_{- 1}^{0} x^{2} (x - 2) d x

- \frac{11}{12}

Dezimale

- 0.91666 \dots

Schritte zur Lösung

\int_{- 1}^{0} x^{2} (x - 2) d x

Multipliziere aus

x^{2} (x - 2) : x^{3} - 2 x^{2}

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{- 1}^{0} x^{3} d x = - \frac{1}{4}

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

= - \frac{1}{4} - \frac{2}{3}

Vereinfache

- \frac{1}{4} - \frac{2}{3} : - \frac{11}{12}

= - \frac{11}{12}

\int_{- 1}^{1} (10 x^{2} + 11) d x

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