integral from 0 to 1 of 10x(5x^2+1)

Lösung

\int_{0}^{1} 10 x (5 x^{2} + 1) d x

\frac{35}{2}

Dezimale

17.5

Schritte zur Lösung

\int_{0}^{1} 10 x (5 x^{2} + 1) d x

Entferne die Konstante:

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

= 10 \cdot \int_{0}^{1} x (5 x^{2} + 1) d x

Multipliziere aus

x (5 x^{2} + 1) : 5 x^{3} + x

= 10 \cdot \int_{0}^{1} 5 x^{3} + x 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

= 10 (\int_{0}^{1} 5 x^{3} d x + \int_{0}^{1} x d x)

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

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

= 10 (\frac{5}{4} + \frac{1}{2})

Vereinfache

10 (\frac{5}{4} + \frac{1}{2}) : \frac{35}{2}

= \frac{35}{2}

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