integral from 0 to 0.1 of xarctan(x)

Lösung

\int_{0}^{0.1} x arctan (x) d x

0.00033 \dots

Schritte zur Lösung

\int_{0}^{0.1} x arctan (x) d x

Wende die partielle Integration an

= [\frac{1}{2} (x^{2} arctan (x) - 2 \cdot \int \frac{x ^{2}}{2 ( x ^{2} + 1 )} d x)]_{0}^{0.1}

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

= [\frac{1}{2} (x^{2} arctan (x) - 2 \cdot \frac{1}{2} (- arctan (x) + x))]_{0}^{0.1}

Vereinfache

[\frac{1}{2} (x^{2} arctan (x) - 2 \cdot \frac{1}{2} (- arctan (x) + x))]_{0}^{0.1} : [\frac{1}{2} (x^{2} arctan (x) + arctan (x) - x)]_{0}^{0.1}

= [\frac{1}{2} (x^{2} arctan (x) + arctan (x) - x)]_{0}^{0.1}

Berechne die Grenzen:

0.00033 \dots

= 0.00033 \dots

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