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Beliebt Rechnen >

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

Lösung

\int_{\frac{π}{2}}^{π} sin (2 x) d x

Lösung

- 1

Schritte zur Lösung

\int_{\frac{π}{2}}^{π} sin (2 x) d x

Wende U-Substitution an

= \int_{π}^{2 π} sin (u) \frac{1}{2} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{π}^{2 π} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [- cos (u)]_{π}^{2 π}

Berechne die Grenzen:

- 2

= \frac{1}{2} (- 2)

Vereinfache

= - 1

Graph

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