integral from 1 to 2 of (e^{2x+1})

Lösung

\int_{1}^{2} (e^{2 x + 1}) d x

\frac{e ^{5} - e ^{3}}{2}

Dezimale

64.16381 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{3}^{5} 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_{3}^{5} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{3}^{5}

Berechne die Grenzen:

e^{5} - e^{3}

= \frac{1}{2} (e^{5} - e^{3})

Vereinfache

= \frac{e ^{5} - e ^{3}}{2}

\int_{0}^{6} 6 sin (0.3 x) d x

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