integral from 0 to infinity of 4/(x^2+1)

Lösung

\int_{0}^{\infty} \frac{4}{x ^{2} + 1} d x

2 π

Dezimale

6.28318 \dots

Schritte zur Lösung

\int_{0}^{\infty} \frac{4}{x ^{2} + 1} d x

Berechne das unbestimmte Integral:

\int \frac{4}{x ^{2} + 1} d x = 4 arctan (x) + C

Berechne die Grenzen:

\int_{0}^{\infty} \frac{4}{x ^{2} + 1} d x = 2 π - 0

= 2 π - 0

Vereinfache

= 2 π

\int_{- 4}^{2} 2 x + 4 d x

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