integral from 0 to 1 of xarccot(x)

Lösung

\int_{0}^{1} x arccot (x) d x

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

\int_{0}^{1} x arccot (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Berechne die Grenzen:

\frac{1}{2}

= \frac{1}{2}

\int_{0}^{6} (x + 1) d x

\int_{1}^{2} \frac{x}{y} + \frac{y}{x} d y

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

\int_{0}^{2} 2 x 12 - x^{2} d x

\int_{0}^{a x} e^{- t^{2}} d t