integral from-1 to 2 of x^3-2x^2-x+2

Lösung

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

\frac{9}{4}

Dezimale

2.25

Schritte zur Lösung

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

\int_{- 1}^{2} x^{3} d x = \frac{15}{4}

\int_{- 1}^{2} 2 x^{2} d x = 6

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

\int_{- 1}^{2} 2 d x = 6

= \frac{15}{4} - 6 - \frac{3}{2} + 6

Vereinfache

\frac{15}{4} - 6 - \frac{3}{2} + 6 : \frac{9}{4}

= \frac{9}{4}