integral from 0 to t of e^{-2(t-x)}

Lösung

\int_{0}^{t} e^{- 2 (t - x)} d x

\frac{1}{2} (1 - e^{- 2 t})

Schritte zur Lösung

\int_{0}^{t} e^{- 2 (t - x)} d x

Wende U-Substitution an

= \int_{- 2 t}^{0} e^{u} \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{- 2 t}^{0} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{- 2 t}^{0}

Berechne die Grenzen:

1 - e^{- 2 t}

= \frac{1}{2} (1 - e^{- 2 t})

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