integral from 0 to 1 of x(x+0.5)

Lösung

\int_{0}^{1} x (x + 0.5) d x

0.58333 \dots

Schritte zur Lösung

\int_{0}^{1} x (x + 0.5) d x

Multipliziere aus

x (x + 0.5) : x^{2} + 0.5 x

= \int_{0}^{1} x^{2} + 0.5 x 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} x^{2} d x + \int_{0}^{1} 0.5 x d x

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

\int_{0}^{1} 0.5 x d x = 0.25

= \frac{1}{3} + 0.25

Vereinfache

= 0.58333 \dots

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