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

Lösung

\int_{\frac{π}{2}}^{2 π} x sin (x) d x

- 2 π - 1

Dezimale

- 7.28318 \dots

Schritte zur Lösung

\int_{\frac{π}{2}}^{2 π} x sin (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

- 2 π - 1

= - 2 π - 1

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