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

Lösung

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

\frac{3 π}{4}

Dezimale

2.35619 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

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

= \frac{π}{4} - (- \frac{π}{2})

Vereinfache

= \frac{3 π}{4}

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