integral from 0 to L of sin((pix)/L)

Lösung

\int_{0}^{L} sin (\frac{π x}{L}) d x

\frac{2 L}{π}

Schritte zur Lösung

\int_{0}^{L} sin (\frac{π x}{L}) d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= \frac{L}{π} [- cos (u)]_{0}^{π}

Berechne die Grenzen:

2

= \frac{L}{π} \cdot 2

Vereinfache

= \frac{2 L}{π}

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