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

Lösung

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

\frac{e ^{\frac{1}{2}}}{2}

Dezimale

0.82436 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= e^{\frac{1}{2}} \cdot \int_{1}^{2} \frac{1}{x ^{2}} d x

Wende die Potenzregel an

= e^{\frac{1}{2}} [- \frac{1}{x}]_{1}^{2}

Berechne die Grenzen:

\frac{1}{2}

= e^{\frac{1}{2}} \frac{1}{2}

Vereinfache

= \frac{e ^{\frac{1}{2}}}{2}

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