integral from 1 to 4 of e^{2x}

Lösung

\int_{1}^{4} e^{2 x} d x

\frac{e ^{8} - e ^{2}}{2}

Dezimale

1486.78446 \dots

Schritte zur Lösung

\int_{1}^{4} e^{2 x} d x

Wende U-Substitution an

= \int_{2}^{8} 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}^{8} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{2}^{8}

Berechne die Grenzen:

e^{8} - e^{2}

= \frac{1}{2} (e^{8} - e^{2})

Vereinfache

= \frac{e ^{8} - e ^{2}}{2}

\int_{0}^{π} π^{2} - x^{2} d x

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