integral from 0 to pi/2 of e^{2x}

Lösung

\int_{0}^{\frac{π}{2}} e^{2 x} d x

\frac{e ^{π} - 1}{2}

Dezimale

11.07034 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} e^{2 x} d x

Wende U-Substitution an

= \int_{0}^{π} 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_{0}^{π} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{0}^{π}

Berechne die Grenzen:

e^{π} - 1

= \frac{1}{2} (e^{π} - 1)

Vereinfache

= \frac{e ^{π} - 1}{2}

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