integral from 0 to 2 of (8x^3-3x^2+6x+2)

Lösung

\int_{0}^{2} (8 x^{3} - 3 x^{2} + 6 x + 2) d x

40

Schritte zur Lösung

\int_{0}^{2} 8 x^{3} - 3 x^{2} + 6 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}^{2} 8 x^{3} d x - \int_{0}^{2} 3 x^{2} d x + \int_{0}^{2} 6 x d x + \int_{0}^{2} 2 d x

\int_{0}^{2} 8 x^{3} d x = 32

\int_{0}^{2} 3 x^{2} d x = 8

\int_{0}^{2} 6 x d x = 12

\int_{0}^{2} 2 d x = 4

= 32 - 8 + 12 + 4

Vereinfache

= 40