integral from 0 to 2 of e^{0.5x}

Lösung

\int_{0}^{2} e^{0.5 x} d x

2 (e - 1)

Dezimale

3.43656 \dots

Schritte zur Lösung

\int_{0}^{2} e^{0.5 x} d x

Wende U-Substitution an

= \int_{0}^{1} e^{u} \frac{1}{0.5} d u

Entferne die Konstante:

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

= \frac{1}{0.5} \cdot \int_{0}^{1} e^{u} d u

Vereinfache

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e - 1

= 2 (e - 1)

\int_{2}^{6} - x^{2} - 8 x - 12 d x

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