integral from 2 to 10 of 1/(1-x^2)

Lösung

\int_{2}^{10} \frac{1}{1 - x ^{2}} d x

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

Dezimale

- 0.44897 \dots

Schritte zur Lösung

\int_{2}^{10} \frac{1}{1 - x ^{2}} d x

Nutze das gemeinsame Integral :

\int \frac{1}{1 - x ^{2}} d x = \frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}

= [\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{2}^{10}

Vereinfache

[\frac{ln ∣ x + 1 ∣}{2} - \frac{ln ∣ x - 1 ∣}{2}]_{2}^{10} : [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{2}^{10}

= [\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]_{2}^{10}

Berechne die Grenzen:

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

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

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