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

Lösung

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

- \frac{4}{3}

Dezimale

- 1.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

x (1 - x)^{2} : x - 2 x^{2} + x^{3}

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

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

\int_{- 1}^{1} 2 x^{2} d x = \frac{4}{3}

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

= 0 - \frac{4}{3} + 0

Vereinfache

= - \frac{4}{3}

x \to 0 + lim (\frac{1}{sin ^{2} ( x )})

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