integral from 3 to infinity of 1/(9+x^2)

Lösung

\int_{3}^{\infty} \frac{1}{9 + x ^{2}} d x

\frac{π}{12}

Dezimale

0.26179 \dots

Schritte zur Lösung

\int_{3}^{\infty} \frac{1}{9 + x ^{2}} d x

Berechne das unbestimmte Integral:

\int \frac{1}{9 + x ^{2}} d x = \frac{1}{3} arctan (\frac{x}{3}) + C

Berechne die Grenzen:

\int_{3}^{\infty} \frac{1}{9 + x ^{2}} d x = \frac{π}{6} - \frac{π}{12}

= \frac{π}{6} - \frac{π}{12}

Vereinfache

= \frac{π}{12}

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