integral from 0 to 1 of 5x^4(8-x^5)

Lösung

\int_{0}^{1} 5 x^{4} (8 - x^{5}) d x

\frac{15}{2}

Dezimale

7.5

Schritte zur Lösung

\int_{0}^{1} 5 x^{4} (8 - x^{5}) d x

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{1} x^{4} (8 - x^{5}) d x

Multipliziere aus

x^{4} (8 - x^{5}) : 8 x^{4} - x^{9}

= 5 \cdot \int_{0}^{1} 8 x^{4} - x^{9} 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

= 5 (\int_{0}^{1} 8 x^{4} d x - \int_{0}^{1} x^{9} d x)

\int_{0}^{1} 8 x^{4} d x = \frac{8}{5}

\int_{0}^{1} x^{9} d x = \frac{1}{10}

= 5 (\frac{8}{5} - \frac{1}{10})

Vereinfache

5 (\frac{8}{5} - \frac{1}{10}) : \frac{15}{2}

= \frac{15}{2}

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