integral from 0 to pi/4 of x^2cos(x)

Lösung

\int_{0}^{\frac{π}{4}} x^{2} cos (x) d x

\frac{π ^{2}}{16 2} - 2 (\frac{1}{2} - \frac{π}{4 2})

Dezimale

0.13268 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} x^{2} cos (x) d x

Wende die partielle Integration an

= [x^{2} sin (x) - \int 2 x sin (x) d x]_{0}^{\frac{π}{4}}

\int 2 x sin (x) d x = 2 (- x cos (x) + sin (x))

= [x^{2} sin (x) - 2 (- x cos (x) + sin (x))]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

\frac{π ^{2}}{16 2} - 2 (\frac{1}{2} - \frac{π}{4 2})

= \frac{π ^{2}}{16 2} - 2 (\frac{1}{2} - \frac{π}{4 2})

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