integral from 0 to pi of x^3cos(x)

Lösung

\int_{0}^{π} x^{3} cos (x) d x

- 3 π^{2} + 12

Dezimale

- 17.60881 \dots

Schritte zur Lösung

\int_{0}^{π} x^{3} cos (x) d x

Wende die partielle Integration an

= [x^{3} sin (x) - \int 3 x^{2} sin (x) d x]_{0}^{π}

\int 3 x^{2} sin (x) d x = 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

= [x^{3} sin (x) - 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))]_{0}^{π}

Berechne die Grenzen:

- 3 π^{2} + 12

= - 3 π^{2} + 12

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