integral from 2 to y of x^2sin(x)

Lösung

\int_{2}^{y} x^{2} sin (x) d x

- y^{2} cos (y) + 2 y sin (y) + 2 cos (y) + 2 cos (2) - 4 sin (2)

Schritte zur Lösung

\int_{2}^{y} x^{2} sin (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

- y^{2} cos (y) + 2 y sin (y) + 2 cos (y) + 2 cos (2) - 4 sin (2)

= - y^{2} cos (y) + 2 y sin (y) + 2 cos (y) + 2 cos (2) - 4 sin (2)

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