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

Lösung

\int_{0}^{π} x^{2} sin (x) d x

π^{2} - 4

Dezimale

5.86960 \dots

Schritte zur Lösung

\int_{0}^{π} x^{2} sin (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

π^{2} - 4

= π^{2} - 4

\int (- \frac{2}{x ^{2}} + 3 x) d x

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