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Beliebt Rechnen >

integral from 0 to 1 of 6(1+sqrt(x))^4

Lösung

\int_{0}^{1} 6 (1 + x)^{4} d x

Lösung

\frac{258}{5}

+1

Dezimale

51.6

Schritte zur Lösung

\int_{0}^{1} 6 (1 + x)^{4} d x

Entferne die Konstante:

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

= 6 \cdot \int_{0}^{1} (1 + x)^{4} d x

Multipliziere aus

(1 + x)^{4} : 1 + 4 x + 6 x + 4 x^{\frac{3}{2}} + x^{2}

= 6 \cdot \int_{0}^{1} 1 + 4 x + 6 x + 4 x^{\frac{3}{2}} + x^{2} 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

= 6 (\int_{0}^{1} 1 d x + \int_{0}^{1} 4 x d x + \int_{0}^{1} 6 x d x + \int_{0}^{1} 4 x^{\frac{3}{2}} d x + \int_{0}^{1} x^{2} d x)

\int_{0}^{1} 1 d x = 1

\int_{0}^{1} 4 x d x = \frac{8}{3}

\int_{0}^{1} 6 x d x = 3

\int_{0}^{1} 4 x^{\frac{3}{2}} d x = \frac{8}{5}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= 6 (1 + \frac{8}{3} + 3 + \frac{8}{5} + \frac{1}{3})

Vereinfache

6 (1 + \frac{8}{3} + 3 + \frac{8}{5} + \frac{1}{3}) : \frac{258}{5}

= \frac{258}{5}

Graph

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