integral from 0 to 2/3 of 4x-6x^2

Lösung

\int_{0}^{\frac{2}{3}} 4 x - 6 x^{2} d x

\frac{8}{27}

Dezimale

0.29629 \dots

Schritte zur Lösung

\int_{0}^{\frac{2}{3}} 4 x - 6 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}^{\frac{2}{3}} 4 x d x - \int_{0}^{\frac{2}{3}} 6 x^{2} d x

\int_{0}^{\frac{2}{3}} 4 x d x = \frac{8}{9}

\int_{0}^{\frac{2}{3}} 6 x^{2} d x = \frac{16}{27}

= \frac{8}{9} - \frac{16}{27}

Vereinfache

\frac{8}{9} - \frac{16}{27} : \frac{8}{27}

= \frac{8}{27}

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