integral from 0 to 4 of (5x-x^2-x)

Lösung

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

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

\int_{0}^{4} 5 x - x^{2} - x d x

Vereinfache

= \int_{0}^{4} - 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

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

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 4 x d x = 32

= - \frac{64}{3} + 32

Vereinfache

- \frac{64}{3} + 32 : \frac{32}{3}

= \frac{32}{3}