integral from 1 to k of k/(2w^2)

Lösung

\int_{1}^{k} \frac{k}{2 w ^{2}} d w

\frac{- 1 + k}{2}

Schritte zur Lösung

\int_{1}^{k} \frac{k}{2 w ^{2}} d w

Entferne die Konstante:

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

= \frac{k}{2} \cdot \int_{1}^{k} \frac{1}{w ^{2}} d w

Wende die Potenzregel an

= \frac{k}{2} [- \frac{1}{w}]_{1}^{k}

Berechne die Grenzen:

- \frac{1}{k} + 1

= \frac{k}{2} (- \frac{1}{k} + 1)

Vereinfache

= \frac{- 1 + k}{2}

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