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

Lösung

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

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

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

\int_{- 1}^{3} 3 x d x = 12

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

= \frac{56}{3} + 12 - 20

Vereinfache

\frac{56}{3} + 12 - 20 : \frac{32}{3}

= \frac{32}{3}

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