integral from-1 to 0 of e^{-2x}

Lösung

\int_{- 1}^{0} e^{- 2 x} d x

\frac{e ^{2} - 1}{2}

Dezimale

3.19452 \dots

Schritte zur Lösung

\int_{- 1}^{0} e^{- 2 x} d x

Wende U-Substitution an

= \int_{2}^{0} - \frac{1}{2} e^{u} d u

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

= - \int_{0}^{2} - \frac{1}{2} e^{u} d u

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{0}^{2} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- \frac{1}{2} [e^{u}]_{0}^{2})

Vereinfache

= \frac{1}{2} [e^{u}]_{0}^{2}

Berechne die Grenzen:

e^{2} - 1

= \frac{1}{2} (e^{2} - 1)

Vereinfache

= \frac{e ^{2} - 1}{2}

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