integral from-1 to 1 of e^{-t}

Lösung

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

e - \frac{1}{e}

Dezimale

2.35040 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

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

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

Berechne die Grenzen:

e - \frac{1}{e}

= e - \frac{1}{e}

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