integral from 0 to 10 of x/(sqrt(16+2x))

Lösung

\int_{0}^{10} \frac{x}{16 + 2 x} d x

\frac{28}{3}

Dezimale

9.33333 \dots

Schritte zur Lösung

\int_{0}^{10} \frac{x}{16 + 2 x} d x

Wende U-Substitution an

= \int_{4}^{6} \frac{u ^{2} - 16}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{4}^{6} u^{2} - 16 d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{4}^{6} u^{2} d u - \int_{4}^{6} 16 d u)

\int_{4}^{6} u^{2} d u = \frac{152}{3}

\int_{4}^{6} 16 d u = 32

= \frac{1}{2} (\frac{152}{3} - 32)

Vereinfache

\frac{1}{2} (\frac{152}{3} - 32) : \frac{28}{3}

= \frac{28}{3}

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