integral from 1 to 4 of (|2-x|)/x

Lösung

\int_{1}^{4} \frac{∣ 2 - x ∣}{x} d x

1

Schritte zur Lösung

\int_{1}^{4} \frac{∣ 2 - x ∣}{x} d x

Entferne die Extremwerte

= \int_{1}^{2} \frac{2 - x}{x} d x + \int_{2}^{4} \frac{- 2 + x}{x} d x

\int_{1}^{2} \frac{2 - x}{x} d x = 2 ln (2) - 1

\int_{2}^{4} \frac{- 2 + x}{x} d x = - 2 ln (2) + 2

= 2 ln (2) - 1 - 2 ln (2) + 2

Vereinfache

2 ln (2) - 1 - 2 ln (2) + 2 : 1

= 1

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