integral from 0 to pi/2 of x^2*sin(x)

Lösung

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

π - 2

Dezimale

1.14159 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

π - 2

= π - 2

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