integral from pi/2 to pi of xcos(x)

Lösung

\int_{\frac{π}{2}}^{π} x cos (x) d x

- 1 - \frac{π}{2}

Dezimale

- 2.57079 \dots

Schritte zur Lösung

\int_{\frac{π}{2}}^{π} x cos (x) d x

Wende die partielle Integration an

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

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

= [x sin (x) - (- cos (x))]_{\frac{π}{2}}^{π}

Vereinfache

= [x sin (x) + cos (x)]_{\frac{π}{2}}^{π}

Berechne die Grenzen:

- 1 - \frac{π}{2}

= - 1 - \frac{π}{2}

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