integral from 0 to 1 of 3/(x^2+1)

Lösung

\int_{0}^{1} \frac{3}{x ^{2} + 1} d x

\frac{3 π}{4}

Dezimale

2.35619 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{3}{x ^{2} + 1} d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{1} \frac{1}{x ^{2} + 1} d x

Nutze das gemeinsame Integral :

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

= 3 [arctan (x)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{4}

= 3 \cdot \frac{π}{4}

Vereinfache

= \frac{3 π}{4}

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