integral from 0 to 0.1 of xarctan(2x)

Lösung

\int_{0}^{0.1} x arctan (2 x) d x

0.00066 \dots

Schritte zur Lösung

\int_{0}^{0.1} x arctan (2 x) d x

Wende die partielle Integration an

= [\frac{1}{2} (x^{2} arctan (2 x) - 2 \cdot \int \frac{x ^{2}}{4 x ^{2} + 1} d x)]_{0}^{0.1}

\int \frac{x ^{2}}{4 x ^{2} + 1} d x = \frac{1}{8} (- arctan (2 x) + 2 x)

= [\frac{1}{2} (x^{2} arctan (2 x) - 2 \cdot \frac{1}{8} (- arctan (2 x) + 2 x))]_{0}^{0.1}

Vereinfache

[\frac{1}{2} (x^{2} arctan (2 x) - 2 \cdot \frac{1}{8} (- arctan (2 x) + 2 x))]_{0}^{0.1} : [0.5 (x^{2} arctan (2 x) - 0.25 (- arctan (2 x) + 2 x))]_{0}^{0.1}

= [0.5 (x^{2} arctan (2 x) - 0.25 (- arctan (2 x) + 2 x))]_{0}^{0.1}

Berechne die Grenzen:

0.00066 \dots

= 0.00066 \dots

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