integral from x to 0 of e^{-9t}

Lösung

\int_{x}^{0} e^{- 9 t} d t

- \frac{1}{9} (1 - e^{- 9 x})

Schritte zur Lösung

\int_{x}^{0} e^{- 9 t} d t

Wende U-Substitution an

= \int_{- 9 x}^{0} - \frac{1}{9} e^{u} d u

Entferne die Konstante:

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

= - \frac{1}{9} \cdot \int_{- 9 x}^{0} e^{u} d u

Nutze das gemeinsame Integral :

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

= - \frac{1}{9} [e^{u}]_{- 9 x}^{0}

Berechne die Grenzen:

1 - e^{- 9 x}

= - \frac{1}{9} (1 - e^{- 9 x})

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