integral from 0 to 3 of 5x(x-4)

Lösung

\int_{0}^{3} 5 x (x - 4) d x

- 45

Schritte zur Lösung

\int_{0}^{3} 5 x (x - 4) d x

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{3} x (x - 4) d x

Multipliziere aus

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

= 5 \cdot \int_{0}^{3} x^{2} - 4 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

= 5 (\int_{0}^{3} x^{2} d x - \int_{0}^{3} 4 x d x)

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

\int_{0}^{3} 4 x d x = 18

= 5 (9 - 18)

Vereinfache

= - 45

\int_{- 1}^{0} \frac{x ^{2} + 4 x - 1}{x + 2} d x

\int_{1}^{2} \frac{ln ( 2 x )}{x} d x

\int_{0}^{2} ln (x + 4) d x

\int_{0}^{1} x 3 x + 1 d x

\int_{0}^{l n (a)} 6 e^{2 x} d x