integral from 0 to 1 of e^{1-x}

Lösung

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

e - 1

Dezimale

1.71828 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

Berechne die Grenzen:

e - 1

= e - 1

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