integral from-1 to 1 of cos(wx)

Lösung

\int_{- 1}^{1} cos (w x) d x

\frac{2 sin ( w )}{w}

Schritte zur Lösung

\int_{- 1}^{1} cos (w x) d x

Wende U-Substitution an

= \int_{- w}^{w} \frac{cos ( u )}{w} d u

Entferne die Konstante:

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

= \frac{1}{w} \cdot \int_{- w}^{w} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{w} [sin (u)]_{- w}^{w}

Berechne die Grenzen:

2 sin (w)

= \frac{1}{w} \cdot 2 sin (w)

Vereinfache

= \frac{2 sin ( w )}{w}

\int_{0}^{1} x e^{x} - \frac{e ^{2 x}}{2} d x

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