integral from-3 to 3 of (9t-t^3)(20t)

Lösung

\int_{- 3}^{3} (9 t - t^{3}) (20 t) d t

1296

Schritte zur Lösung

\int_{- 3}^{3} (9 t - t^{3}) \cdot 20 t d t

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 20 \cdot \int_{- 3}^{3} (9 t - t^{3}) t d t

Multipliziere aus

(9 t - t^{3}) t : 9 t^{2} - t^{4}

= 20 \cdot \int_{- 3}^{3} 9 t^{2} - t^{4} d t

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 20 (\int_{- 3}^{3} 9 t^{2} d t - \int_{- 3}^{3} t^{4} d t)

\int_{- 3}^{3} 9 t^{2} d t = 162

\int_{- 3}^{3} t^{4} d t = \frac{486}{5}

= 20 (162 - \frac{486}{5})

Vereinfache

20 (162 - \frac{486}{5}) : 1296

= 1296

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