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Beliebt Rechnen >

integral from 0 to pi/4 of sin(2x)

Lösung

\int_{0}^{\frac{π}{4}} sin (2 x) d x

Lösung

\frac{1}{2}

+1

Dezimale

0.5

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} sin (2 x) d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

1

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

Vereinfache

= \frac{1}{2}

Graph

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