integral from e^{-1} to e of |ln(x)|

Lösung

\int_{e^{- 1}}^{e} ∣ ln (x) ∣ d x

- \frac{2}{e} + 2

Dezimale

1.26424 \dots

Schritte zur Lösung

\int_{e^{- 1}}^{e} ∣ ln (x) ∣ d x

Wende U-Substitution an

= \int_{- 1}^{1} ∣ u ∣ e^{u} d u

Entferne die Extremwerte

= \int_{- 1}^{0} (- u) e^{u} d u + \int_{0}^{1} u e^{u} d u

\int_{- 1}^{0} (- u) e^{u} d u = 1 - \frac{2}{e}

\int_{0}^{1} u e^{u} d u = 1

= 1 - \frac{2}{e} + 1

Vereinfache

= - \frac{2}{e} + 2

\int_{- 1}^{2} ∣ x - 1 ∣ d x

\int_{- 2}^{2} x ln (1 + x^{4}) d x

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

\int_{\frac{- 1}{8}}^{\frac{1}{8}} sin (2 π x) d x