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

Lösung

\int_{0}^{1} (\frac{2}{1 + x ^{2}}) d x

\frac{π}{2}

Dezimale

1.57079 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= 2 [arctan (x)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= 2 \cdot \frac{π}{4}

Vereinfache

= \frac{π}{2}

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