integral from 2 to 3 of 3/(1+x^2)

Lösung

\int_{2}^{3} \frac{3}{1 + x ^{2}} d x

3 (arctan (3) - arctan (2))

Dezimale

0.42569 \dots

Schritte zur Lösung

\int_{2}^{3} \frac{3}{1 + x ^{2}} d x

Entferne die Konstante:

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

= 3 \cdot \int_{2}^{3} \frac{1}{1 + x ^{2}} d x

Nutze das gemeinsame Integral :

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

= 3 [arctan (x)]_{2}^{3}

Berechne die Grenzen:

arctan (3) - arctan (2)

= 3 (arctan (3) - arctan (2))

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