integral from 0 to pi of 2/(x^2+1)

Lösung

\int_{0}^{π} \frac{2}{x ^{2} + 1} d x

2 arctan (π)

Dezimale

2.52525 \dots

Schritte zur Lösung

\int_{0}^{π} \frac{2}{x ^{2} + 1} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{π} \frac{1}{x ^{2} + 1} d x

Nutze das gemeinsame Integral :

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

= 2 [arctan (x)]_{0}^{π}

Berechne die Grenzen:

arctan (π)

= 2 arctan (π)

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