integral from 0 to 2 of-2x(2+x^5)

Lösung

\int_{0}^{2} - 2 x (2 + x^{5}) d x

- \frac{312}{7}

Dezimale

- 44.57142 \dots

Schritte zur Lösung

\int_{0}^{2} - 2 x (2 + x^{5}) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int_{0}^{2} x (2 + x^{5}) d x

Multipliziere aus

x (2 + x^{5}) : 2 x + x^{6}

= - 2 \cdot \int_{0}^{2} 2 x + x^{6} 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

= - 2 (\int_{0}^{2} 2 x d x + \int_{0}^{2} x^{6} d x)

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

\int_{0}^{2} x^{6} d x = \frac{128}{7}

= - 2 (4 + \frac{128}{7})

Vereinfache

- 2 (4 + \frac{128}{7}) : - \frac{312}{7}

= - \frac{312}{7}

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