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

Lösung

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

4

Schritte zur Lösung

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

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

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

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

\int_{- 1}^{1} 3 d x = 6

= 0 - 2 - 0 + 6

Vereinfache

= 4