integral from 0 to 1 of (1-cos(x))/(x^2)

Lösung

\int_{0}^{1} \frac{1 - cos ( x )}{x ^{2}} d x

0.48638 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{1 - cos ( x )}{x ^{2}} d x

Wende die partielle Integration an

= [- \frac{1 - cos ( x )}{x} - \int - \frac{sin ( x )}{x} d x]_{0}^{1}

\int - \frac{sin ( x )}{x} d x = - Si (x)

= [- \frac{1 - cos ( x )}{x} - (- Si (x))]_{0}^{1}

Vereinfache

= [- \frac{1 - cos ( x )}{x} + Si (x)]_{0}^{1}

Berechne die Grenzen:

0.48638 \dots

= 0.48638 \dots

\int_{0}^{\frac{π}{2}} \frac{1}{1 + sin ( x )} d x

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