integral from 0 to 1 of 1/(5x-10)

Lösung

\int_{0}^{1} \frac{1}{5 x - 10} d x

- \frac{1}{5} ln (2)

Dezimale

- 0.13862 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1}{5 x - 10} d x

Wende U-Substitution an

= \int_{- 10}^{- 5} \frac{1}{5 u} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{- 10}^{- 5} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} [ln ∣ u ∣]_{- 10}^{- 5}

Berechne die Grenzen:

ln (5) - ln (10)

= \frac{1}{5} (ln (5) - ln (10))

Vereinfache

= - \frac{1}{5} ln (2)

\int_{0}^{x} t^{3} d t

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\int_{1}^{\infty} \frac{1}{n ^{4}}