integral from 0 to 1 of (arccos(x))^2

Lösung

\int_{0}^{1} (arccos (x))^{2} d x

- 2 + π

Dezimale

1.14159 \dots

Schritte zur Lösung

\int_{0}^{1} (arccos (x))^{2} d x

Vereinfache

= \int_{0}^{1} arccos^{2} (x) d x

Wende die partielle Integration an

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

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

= [x arccos^{2} (x) - 2 (arccos (x) 1 - x^{2} + x)]_{0}^{1}

Berechne die Grenzen:

- 2 + π

= - 2 + π

\int_{0}^{2 π} x (cos (x))^{2} d x

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