integral from 0 to 2 of-4x^2+8x^3

Lösung

\int_{0}^{2} - 4 x^{2} + 8 x^{3} d x

\frac{64}{3}

Dezimale

21.33333 \dots

Schritte zur Lösung

\int_{0}^{2} - 4 x^{2} + 8 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}^{2} 4 x^{2} d x + \int_{0}^{2} 8 x^{3} d x

\int_{0}^{2} 4 x^{2} d x = \frac{32}{3}

\int_{0}^{2} 8 x^{3} d x = 32

= - \frac{32}{3} + 32

Vereinfache

- \frac{32}{3} + 32 : \frac{64}{3}

= \frac{64}{3}

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