integral from 0 to pi/2 of sin(x/2)

Lösung

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

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

Dezimale

0.58578 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{\frac{π}{4}} sin (u) \cdot 2 d u

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{\frac{π}{4}} sin (u) d u

Nutze das gemeinsame Integral :

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

= 2 [- cos (u)]_{0}^{\frac{π}{4}}

Berechne die Grenzen:

- \frac{1}{2} + 1

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

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