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

Lösung

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

21

Schritte zur Lösung

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

Multipliziere aus

(2 x + 1)^{2} : 4 x^{2} + 4 x + 1

= \int_{- 1}^{2} 4 x^{2} + 4 x + 1 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} 4 x^{2} d x + \int_{- 1}^{2} 4 x d x + \int_{- 1}^{2} 1 d x

\int_{- 1}^{2} 4 x^{2} d x = 12

\int_{- 1}^{2} 4 x d x = 6

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

= 12 + 6 + 3

Vereinfache

= 21

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