integral from-2 to 2 of x^3+3x^2-2x+4

Lösung

\int_{- 2}^{2} x^{3} + 3 x^{2} - 2 x + 4 d x

32

Schritte zur Lösung

\int_{- 2}^{2} x^{3} + 3 x^{2} - 2 x + 4 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_{- 2}^{2} x^{3} d x + \int_{- 2}^{2} 3 x^{2} d x - \int_{- 2}^{2} 2 x d x + \int_{- 2}^{2} 4 d x

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

\int_{- 2}^{2} 3 x^{2} d x = 16

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

\int_{- 2}^{2} 4 d x = 16

= 0 + 16 - 0 + 16

Vereinfache

= 32

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