integral from 0.25 to 0.5 of 20x^3(1-x)

Lösung

\int_{0.25}^{0.5} 20 x^{3} (1 - x) d x

0.171875

Schritte zur Lösung

\int_{0.25}^{0.5} 20 x^{3} (1 - x) d x

Entferne die Konstante:

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

= 20 \cdot \int_{0.25}^{0.5} x^{3} (1 - x) d x

Multipliziere aus

x^{3} (1 - x) : x^{3} - x^{4}

= 20 \cdot \int_{0.25}^{0.5} x^{3} - 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

= 20 (\int_{0.25}^{0.5} x^{3} d x - \int_{0.25}^{0.5} x^{4} d x)

\int_{0.25}^{0.5} x^{3} d x = 0.0146484375

\int_{0.25}^{0.5} x^{4} d x = 0.0060546875

= 20 (0.0146484375 - 0.00605 \dots)

Vereinfache

= 0.171875

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