integral from 0 to 1 of x^2+x-2

Lösung

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

- \frac{7}{6}

Dezimale

- 1.16666 \dots

Schritte zur Lösung

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

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

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

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

= \frac{1}{3} + \frac{1}{2} - 2

Vereinfache

\frac{1}{3} + \frac{1}{2} - 2 : - \frac{7}{6}

= - \frac{7}{6}