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

Lösung

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

\frac{45}{4}

Dezimale

11.25

Schritte zur Lösung

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

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

\int_{- 3}^{0} 2 x^{2} d x = 18

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

= - \frac{81}{4} + 18 - (- \frac{27}{2})

Vereinfache

- \frac{81}{4} + 18 - (- \frac{27}{2}) : \frac{45}{4}

= \frac{45}{4}

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