integral from 0 to x^6 of e^{-t}

Lösung

\int_{0}^{x^{6}} e^{- t} d t

- e^{- x^{6}} + 1

Schritte zur Lösung

\int_{0}^{x^{6}} e^{- t} d t

Wende U-Substitution an

= \int_{0}^{- x^{6}} - e^{u} d u

Entferne die Konstante:

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

= - \int_{0}^{- x^{6}} e^{u} d u

Nutze das gemeinsame Integral :

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

= - [e^{u}]_{0}^{- x^{6}}

Berechne die Grenzen:

e^{- x^{6}} - 1

= - (e^{- x^{6}} - 1)

Vereinfache

= - e^{- x^{6}} + 1

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