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

Lösung

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

1296

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Multipliziere aus

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

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

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

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

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

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

Vereinfache

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

= 1296

\int_{0}^{\frac{π}{2}} 6 cos (x) d x

\int_{1}^{x^{2}} (t - 4) e^{- t^{2}} d t

\int_{0}^{6} (16 - 2 x)^{\frac{1}{2}} d x

\int_{0}^{4} \frac{1}{96} x y d x

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