integral from-v to v of e^{u/v}

Lösung

\int_{- v}^{v} e^{\frac{u}{v}} d u

v (e - \frac{1}{e})

Schritte zur Lösung

\int_{- v}^{v} e^{\frac{u}{v}} d u

Wende U-Substitution an

= \int_{- 1}^{1} e^{w} v d w

Entferne die Konstante:

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

= v \cdot \int_{- 1}^{1} e^{w} d w

Nutze das gemeinsame Integral :

\int e^{w} d w = e^{w}

= v [e^{w}]_{- 1}^{1}

Berechne die Grenzen:

e - \frac{1}{e}

= v (e - \frac{1}{e})

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