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Beliebt Rechnen >

integral from-1 to 1 of (14-12x)^{-1}

Lösung

\int_{- 1}^{1} (14 - 12 x)^{- 1} d x

Lösung

\frac{1}{12} ln (13)

+1

Dezimale

0.21374 \dots

Schritte zur Lösung

\int_{- 1}^{1} (14 - 12 x)^{- 1} d x

Wende Exponentenregel an:

a^{- 1} = \frac{1}{a}

= \int_{- 1}^{1} \frac{1}{14 - 12 x} d x

Wende U-Substitution an

= \int_{26}^{2} - \frac{1}{12 u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{2}^{26} - \frac{1}{12 u} d u

Entferne die Konstante:

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

= - (- \frac{1}{12} \cdot \int_{2}^{26} \frac{1}{u} d u)

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{12} [ln ∣ u ∣]_{2}^{26})

Vereinfache

= \frac{1}{12} [ln ∣ u ∣]_{2}^{26}

Berechne die Grenzen:

ln (26) - ln (2)

= \frac{1}{12} (ln (26) - ln (2))

Vereinfache

= \frac{1}{12} ln (13)

Graph

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