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Beliebt Rechnen >

integral from 6 to 11 of 10arccot(x)

Lösung

\int_{6}^{11} 10 arccot (x) d x

Lösung

10 (11 arccot (11) - 6 arccot (6) + \frac{ln ( 122 ) - ln ( 37 )}{2})

+1

Dezimale

6.02918 \dots

Schritte zur Lösung

\int_{6}^{11} 10 arccot (x) d x

Entferne die Konstante:

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

= 10 \cdot \int_{6}^{11} arccot (x) d x

Wende die partielle Integration an

= 10 [x arccot (x) - \int - \frac{x}{x ^{2} + 1} d x]_{6}^{11}

\int - \frac{x}{x ^{2} + 1} d x = - \frac{1}{2} ln x^{2} + 1

= 10 [x arccot (x) - (- \frac{1}{2} ln x^{2} + 1)]_{6}^{11}

Vereinfache

= 10 [x arccot (x) + \frac{1}{2} ln x^{2} + 1]_{6}^{11}

Berechne die Grenzen:

11 arccot (11) - 6 arccot (6) + \frac{ln ( 122 ) - ln ( 37 )}{2}

= 10 (11 arccot (11) - 6 arccot (6) + \frac{ln ( 122 ) - ln ( 37 )}{2})

Graph

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