integral from 0 to 5 of (x-3)(x-1)

Lösung

\int_{0}^{5} (x - 3) (x - 1) d x

\frac{20}{3}

Dezimale

6.66666 \dots

Schritte zur Lösung

\int_{0}^{5} (x - 3) (x - 1) d x

Multipliziere aus

(x - 3) (x - 1) : x^{2} - 4 x + 3

= \int_{0}^{5} x^{2} - 4 x + 3 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}^{5} x^{2} d x - \int_{0}^{5} 4 x d x + \int_{0}^{5} 3 d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} 4 x d x = 50

\int_{0}^{5} 3 d x = 15

= \frac{125}{3} - 50 + 15

Vereinfache

\frac{125}{3} - 50 + 15 : \frac{20}{3}

= \frac{20}{3}

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