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

Lösung

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

129

Schritte zur Lösung

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

Multipliziere aus

(x - 8)^{2} : x^{2} - 16 x + 64

= \int_{0}^{3} x^{2} - 16 x + 64 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}^{3} x^{2} d x - \int_{0}^{3} 16 x d x + \int_{0}^{3} 64 d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 16 x d x = 72

\int_{0}^{3} 64 d x = 192

= 9 - 72 + 192

Vereinfache

= 129

\int_{2}^{6} - x^{2} + 8 x - 12 d x

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

\int_{0}^{2} π x^{6} d x

\int_{0}^{y} \frac{1}{2} d x

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