integral from 0 to pi/2 of 2sin(2θ)

Lösung

\int_{0}^{\frac{π}{2}} 2 sin (2 θ) d θ

2

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 2 sin (2 θ) d θ

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{\frac{π}{2}} sin (2 θ) d θ

Wende U-Substitution an

= 2 \cdot \int_{0}^{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

= 2 \cdot \frac{1}{2} \cdot \int_{0}^{π} sin (u) d u

Nutze das gemeinsame Integral :

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

= 2 \cdot \frac{1}{2} [- cos (u)]_{0}^{π}

Vereinfache

2 \cdot \frac{1}{2} [- cos (u)]_{0}^{π} : [- cos (u)]_{0}^{π}

= [- cos (u)]_{0}^{π}

Berechne die Grenzen:

2

= 2

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