integral from 0 to 1 of x(x^2-x)

Lösung

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

- \frac{1}{12}

Dezimale

- 0.08333 \dots

Schritte zur Lösung

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

Multipliziere aus

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

= \int_{0}^{1} x^{3} - x^{2} 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}^{1} x^{3} d x - \int_{0}^{1} x^{2} d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= \frac{1}{4} - \frac{1}{3}

Vereinfache

\frac{1}{4} - \frac{1}{3} : - \frac{1}{12}

= - \frac{1}{12}