integral from 0 to a of x(a-x)

Lösung

\int_{0}^{a} x (a - x) d x

\frac{a ^{3}}{2} - \frac{a ^{3}}{3}

Schritte zur Lösung

\int_{0}^{a} x (a - x) d x

Multipliziere aus

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

= \int_{0}^{a} a 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}^{a} a x d x - \int_{0}^{a} x^{2} d x

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

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

= \frac{a ^{3}}{2} - \frac{a ^{3}}{3}

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