integral from-2 to 3 of x^2sin(x)

Lösung

\int_{- 2}^{3} x^{2} sin (x) d x

- 7 cos (3) + 6 sin (3) + 2 cos (2) - 4 sin (2)

Dezimale

3.30718 \dots

Schritte zur Lösung

\int_{- 2}^{3} x^{2} sin (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

- 7 cos (3) + 6 sin (3) + 2 cos (2) - 4 sin (2)

= - 7 cos (3) + 6 sin (3) + 2 cos (2) - 4 sin (2)

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