integral from-2 to 2 of e^{4x}

Lösung

\int_{- 2}^{2} e^{4 x} d x

\frac{e ^{16} - 1}{4 e ^{8}}

Dezimale

745.23941 \dots

Schritte zur Lösung

\int_{- 2}^{2} e^{4 x} d x

Wende U-Substitution an

= \int_{- 8}^{8} e^{u} \frac{1}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{- 8}^{8} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{4} [e^{u}]_{- 8}^{8}

Berechne die Grenzen:

e^{8} - \frac{1}{e ^{8}}

= \frac{1}{4} (e^{8} - \frac{1}{e ^{8}})

Vereinfache

= \frac{e ^{16} - 1}{4 e ^{8}}

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