integral from 0 to pi/2 of-sin(2t-pi/3)

Lösung

\int_{0}^{\frac{π}{2}} - sin (2 t - \frac{π}{3}) d t

- \frac{1}{2}

Dezimale

- 0.5

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} - sin (2 t - \frac{π}{3}) d t

Entferne die Konstante:

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

= - \int_{0}^{\frac{π}{2}} sin (2 t - \frac{π}{3}) d t

Wende U-Substitution an

= - \int_{- \frac{π}{3}}^{π - \frac{π}{3}} 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_{- \frac{π}{3}}^{π - \frac{π}{3}} sin (u) d u

Nutze das gemeinsame Integral :

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

= - \frac{1}{2} [- cos (u)]_{- \frac{π}{3}}^{π - \frac{π}{3}}

Berechne die Grenzen:

1

= - \frac{1}{2} \cdot 1

Vereinfache

= - \frac{1}{2}

\int_{1}^{3} 9 - x^{2} d x

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