integral from 0 to pi of sin(mx)

Lösung

\int_{0}^{π} sin (m x) d x

\frac{- cos ( πm ) + 1}{m}

Schritte zur Lösung

\int_{0}^{π} sin (m x) d x

Wende U-Substitution an

= \int_{0}^{mπ} \frac{sin ( u )}{m} d u

Entferne die Konstante:

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

= \frac{1}{m} \cdot \int_{0}^{mπ} sin (u) d u

Nutze das gemeinsame Integral :

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

= \frac{1}{m} [- cos (u)]_{0}^{mπ}

Berechne die Grenzen:

- cos (πm) + 1

= \frac{1}{m} (- cos (πm) + 1)

Vereinfache

= \frac{- cos ( πm ) + 1}{m}

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