integral from 0 to 3 of 5/(x^2+1)

Lösung

\int_{0}^{3} \frac{5}{x ^{2} + 1} d x

5 arctan (3)

Dezimale

6.24522 \dots

Schritte zur Lösung

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

Nutze das gemeinsame Integral :

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

= 5 [arctan (x)]_{0}^{3}

Berechne die Grenzen:

arctan (3)

= 5 arctan (3)

\int_{- 1}^{y - 1} \frac{3}{2} x^{2} d x

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\int_{0}^{1} 3 x sin (π) x d x