integral from 0 to 1 of x(4-x)

Lösung

\int_{0}^{1} x (4 - x) d x

\frac{5}{3}

Dezimale

1.66666 \dots

Schritte zur Lösung

\int_{0}^{1} x (4 - x) d x

Multipliziere aus

x (4 - x) : 4 x - x^{2}

= \int_{0}^{1} 4 x - x^{2} 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}^{1} 4 x d x - \int_{0}^{1} x^{2} d x

\int_{0}^{1} 4 x d x = 2

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= 2 - \frac{1}{3}

Vereinfache

2 - \frac{1}{3} : \frac{5}{3}

= \frac{5}{3}

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