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

Lösung

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

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

Dezimale

0.43233 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

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

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

Vereinfache

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

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