integral from 4 to 5 of x/(sqrt(2x-6))

Lösung

\int_{4}^{5} \frac{x}{2 x - 6} d x

\frac{2 ( 11 - 5 2 )}{3}

Dezimale

2.61928 \dots

Schritte zur Lösung

\int_{4}^{5} \frac{x}{2 x - 6} d x

Wende U-Substitution an

= \int_{2}^{2} \frac{u ^{2} + 6}{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_{2}^{2} u^{2} + 6 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_{2}^{2} u^{2} d u + \int_{2}^{2} 6 d u)

\int_{2}^{2} u^{2} d u = \frac{8 - 2 2}{3}

\int_{2}^{2} 6 d u = 12 - 62

= \frac{1}{2} (\frac{8 - 2 2}{3} + 12 - 62)

Vereinfache

\frac{1}{2} (\frac{8 - 2 2}{3} + 12 - 62) : \frac{2 ( 11 - 5 2 )}{3}

= \frac{2 ( 11 - 5 2 )}{3}

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