integral from 0 to 3 of x^3-3x^2-x+3

Lösung

\int_{0}^{3} x^{3} - 3 x^{2} - x + 3 d x

- \frac{9}{4}

Dezimale

- 2.25

Schritte zur Lösung

\int_{0}^{3} x^{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} x^{3} d x - \int_{0}^{3} 3 x^{2} d x - \int_{0}^{3} x d x + \int_{0}^{3} 3 d x

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

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

\int_{0}^{3} x d x = \frac{9}{2}

\int_{0}^{3} 3 d x = 9

= \frac{81}{4} - 27 - \frac{9}{2} + 9

Vereinfache

\frac{81}{4} - 27 - \frac{9}{2} + 9 : - \frac{9}{4}

= - \frac{9}{4}

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