integral from-1 to 1 of 5/8 (1-x^4)

Lösung

\int_{- 1}^{1} \frac{5}{8} (1 - x^{4}) d x

1

Schritte zur Lösung

\int_{- 1}^{1} \frac{5}{8} (1 - x^{4}) d x

Entferne die Konstante:

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

= \frac{5}{8} \cdot \int_{- 1}^{1} 1 - x^{4} 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

= \frac{5}{8} (\int_{- 1}^{1} 1 d x - \int_{- 1}^{1} x^{4} d x)

\int_{- 1}^{1} 1 d x = 2

\int_{- 1}^{1} x^{4} d x = \frac{2}{5}

= \frac{5}{8} (2 - \frac{2}{5})

Vereinfache

\frac{5}{8} (2 - \frac{2}{5}) : 1

= 1

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