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

Lösung

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

d (\frac{x ^{3} + 1}{3} - \frac{x ^{2} - 1}{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

= d \cdot \int_{- 1}^{x} x^{2} - 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

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

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

\int_{- 1}^{x} x d x = \frac{x ^{2} - 1}{2}

= d (\frac{x ^{3} + 1}{3} - \frac{x ^{2} - 1}{2})