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

Lösung

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

- \frac{73}{12}

Dezimale

- 6.08333 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

\int_{- 3}^{- 2} x^{3} d x = - \frac{65}{4}

\int_{- 3}^{- 2} 2 x^{2} d x = \frac{38}{3}

\int_{- 3}^{- 2} x d x = - \frac{5}{2}

= - \frac{65}{4} + \frac{38}{3} - \frac{5}{2}

Vereinfache

- \frac{65}{4} + \frac{38}{3} - \frac{5}{2} : - \frac{73}{12}

= - \frac{73}{12}

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