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

Lösung

\int_{0}^{\infty} \frac{2}{1 + t ^{2}} d t

π

Dezimale

3.14159 \dots

Schritte zur Lösung

\int_{0}^{\infty} \frac{2}{1 + t ^{2}} d t

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

\int_{0}^{\infty} \frac{2}{1 + t ^{2}} d t = π - 0

= π - 0

Vereinfache

= π

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