integral from 2 to 4 of xcos(x)

Lösung

\int_{2}^{4} x cos (x) d x

4 sin (4) + cos (4) - 2 sin (2) - cos (2)

Dezimale

- 5.08330 \dots

Schritte zur Lösung

\int_{2}^{4} x cos (x) d x

Wende die partielle Integration an

= [x sin (x) - \int sin (x) d x]_{2}^{4}

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

= [x sin (x) - (- cos (x))]_{2}^{4}

Vereinfache

= [x sin (x) + cos (x)]_{2}^{4}

Berechne die Grenzen:

4 sin (4) + cos (4) - 2 sin (2) - cos (2)

= 4 sin (4) + cos (4) - 2 sin (2) - cos (2)

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