integral from-1 to 3 of (-x^3+3x^2-5)

Lösung

\int_{- 1}^{3} (- x^{3} + 3 x^{2} - 5) d x

- 12

Schritte zur Lösung

\int_{- 1}^{3} - x^{3} + 3 x^{2} - 5 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} x^{3} d x + \int_{- 1}^{3} 3 x^{2} d x - \int_{- 1}^{3} 5 d x

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

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} 5 d x = 20

= - 20 + 28 - 20

Vereinfache

= - 12

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