integral from 2 to-2 of (9r+8)^2

Lösung

\int_{2}^{- 2} (9 r + 8)^{2} d r

- 688

Schritte zur Lösung

\int_{2}^{- 2} (9 r + 8)^{2} d r

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 2}^{2} (9 r + 8)^{2} d r

Multipliziere aus

(9 r + 8)^{2} : 81 r^{2} + 144 r + 64

= - \int_{- 2}^{2} 81 r^{2} + 144 r + 64 d r

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} 81 r^{2} d r + \int_{- 2}^{2} 144 r d r + \int_{- 2}^{2} 64 d r)

\int_{- 2}^{2} 81 r^{2} d r = 432

\int_{- 2}^{2} 144 r d r = 0

\int_{- 2}^{2} 64 d r = 256

= - (432 + 0 + 256)

Vereinfache

= - 688

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