integral from-1 to 1 of (1+x^2)^{-1}

Lösung

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

\frac{π}{2}

Dezimale

1.57079 \dots

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Nutze das gemeinsame Integral :

\int \frac{1}{1 + x ^{2}} d x = arctan (x)

= [arctan (x)]_{- 1}^{1}

Berechne die Grenzen:

\frac{π}{2}

= \frac{π}{2}

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