integral from 0 to 3 of 2x(x-6)

Lösung

\int_{0}^{3} 2 x (x - 6) d x

- 36

Schritte zur Lösung

\int_{0}^{3} 2 x (x - 6) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{3} x (x - 6) d x

Multipliziere aus

x (x - 6) : x^{2} - 6 x

= 2 \cdot \int_{0}^{3} x^{2} - 6 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

= 2 (\int_{0}^{3} x^{2} d x - \int_{0}^{3} 6 x d x)

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

\int_{0}^{3} 6 x d x = 27

= 2 (9 - 27)

Vereinfache

= - 36

\int_{- 1}^{0} 2 x^{2} (4 x^{3} - 1)^{3} d x

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

\int_{0}^{4} x^{2} e^{x} d x

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

\int_{4}^{8} 10 - x d x