integral from 0 to 4 of (x-3)^2

Lösung

\int_{0}^{4} (x - 3)^{2} d x

\frac{28}{3}

Dezimale

9.33333 \dots

Schritte zur Lösung

\int_{0}^{4} (x - 3)^{2} d x

Multipliziere aus

(x - 3)^{2} : x^{2} - 6 x + 9

= \int_{0}^{4} x^{2} - 6 x + 9 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}^{4} x^{2} d x - \int_{0}^{4} 6 x d x + \int_{0}^{4} 9 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 6 x d x = 48

\int_{0}^{4} 9 d x = 36

= \frac{64}{3} - 48 + 36

Vereinfache

\frac{64}{3} - 48 + 36 : \frac{28}{3}

= \frac{28}{3}

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