integral from 0 to 3 of x(3x-x^2)

Lösung

\int_{0}^{3} x (3 x - x^{2}) d x

\frac{27}{4}

Dezimale

6.75

Schritte zur Lösung

\int_{0}^{3} x (3 x - x^{2}) d x

Multipliziere aus

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

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

\int_{0}^{3} 3 x^{2} d x = 27

\int_{0}^{3} x^{3} d x = \frac{81}{4}

= 27 - \frac{81}{4}

Vereinfache

27 - \frac{81}{4} : \frac{27}{4}

= \frac{27}{4}

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