integral from 1 to 5 of (e^{1/x})/(x^2)

Lösung

\int_{1}^{5} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

e - 5 e

Dezimale

1.49687 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

Wende U-Substitution an

= \int_{1}^{\frac{1}{5}} - e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{\frac{1}{5}}^{1} - e^{u} d u

Entferne die Konstante:

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

= - (- \int_{\frac{1}{5}}^{1} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- [e^{u}]_{\frac{1}{5}}^{1})

Vereinfache

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

Berechne die Grenzen:

e - 5 e

= e - 5 e

\int_{0}^{2} 5 t cos (π t) d t

\int_{0}^{2} 5 x cos (π x) d x

\int_{1}^{2} 2 - x d x

\int_{0}^{\frac{1}{2}} sin (2 π x) d x

\int_{0}^{\frac{π}{2}} sin^{2} (θ) d θ