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

Lösung

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

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

\int_{- 1}^{3} x^{3} d x = 20

\int_{- 1}^{3} 2 x^{2} d x = \frac{56}{3}

= 20 - \frac{56}{3}

Vereinfache

20 - \frac{56}{3} : \frac{4}{3}

= \frac{4}{3}

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