integral from x to 1 of e^{(1-x)}

Lösung

\int_{x}^{1} e^{(1 - x)} d x

- 1 + e^{1 - x}

Schritte zur Lösung

\int_{x}^{1} e^{1 - x} d x

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

1 - e^{1 - x}

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

Vereinfache

= - 1 + e^{1 - x}

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