integral from 0 to pi of cos(kx)

Lösung

\int_{0}^{π} cos (k x) d x

0

Schritte zur Lösung

\int_{0}^{π} cos (k x) d x

Wende U-Substitution an

= \int_{0}^{kπ} \frac{cos ( u )}{k} d u

Entferne die Konstante:

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

= \frac{1}{k} \cdot \int_{0}^{kπ} cos (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{k} [sin (u)]_{0}^{kπ}

Berechne die Grenzen:

0

= \frac{1}{k} \cdot 0

Vereinfache

= 0

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