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

Lösung

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

2 π

Dezimale

6.28318 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 4 \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)

= 4 [arctan (x)]_{- 1}^{1}

Berechne die Grenzen:

\frac{π}{2}

= 4 \cdot \frac{π}{2}

Vereinfache

= 2 π

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