integral from 0 to 2 of x^2-(4x-x^2)

Lösung

\int_{0}^{2} x^{2} - (4 x - x^{2}) d x

- \frac{8}{3}

Dezimale

- 2.66666 \dots

Schritte zur Lösung

\int_{0}^{2} x^{2} - (4 x - x^{2}) d x

Vereinfache

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

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

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

= \frac{16}{3} - 8

Vereinfache

\frac{16}{3} - 8 : - \frac{8}{3}

= - \frac{8}{3}

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