integral from-1 to 1 of x^3sin(x)

Lösung

\int_{- 1}^{1} x^{3} sin (x) d x

10 cos (1) - 6 sin (1)

Dezimale

0.35419 \dots

Schritte zur Lösung

\int_{- 1}^{1} x^{3} sin (x) d x

Wende die partielle Integration an

= [- x^{3} cos (x) - \int - 3 x^{2} cos (x) d x]_{- 1}^{1}

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

= [- x^{3} cos (x) - (- 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x))))]_{- 1}^{1}

Vereinfache

= [- x^{3} cos (x) + 3 (x^{2} sin (x) - 2 (- x cos (x) + sin (x)))]_{- 1}^{1}

Berechne die Grenzen:

10 cos (1) - 6 sin (1)

= 10 cos (1) - 6 sin (1)

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