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

Lösung

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

\frac{π}{6}

Dezimale

0.52359 \dots

Schritte zur Lösung

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

Nutze das gemeinsame Integral :

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

= 2 [arctan (x)]_{1}^{3}

Berechne die Grenzen:

\frac{π}{12}

= 2 \cdot \frac{π}{12}

Vereinfache

= \frac{π}{6}

\int_{- 1}^{1} \frac{x + 5}{x ^{2} + 2 x + 5} d x

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