integral from-1 to 1 of (5/(x^2+1))

Lösung

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

\frac{5 π}{2}

Dezimale

7.85398 \dots

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Nutze das gemeinsame Integral :

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

= 5 [arctan (x)]_{- 1}^{1}

Berechne die Grenzen:

\frac{π}{2}

= 5 \cdot \frac{π}{2}

Vereinfache

= \frac{5 π}{2}

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