integral from 1 to 4 of (e^{1/x})/(x^2)

Lösung

\int_{1}^{4} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

e - 4 e

Dezimale

1.43425 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

Wende U-Substitution an

= \int_{1}^{\frac{1}{4}} - e^{u} d u

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

= - \int_{\frac{1}{4}}^{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}{4}}^{1} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- [e^{u}]_{\frac{1}{4}}^{1})

Vereinfache

= [e^{u}]_{\frac{1}{4}}^{1}

Berechne die Grenzen:

e - 4 e

= e - 4 e

\int_{2}^{5} x^{2} + 5 x d x

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

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

\int_{0}^{2} 5 t cos (π t) d t

\int_{0}^{2} 5 x cos (π x) d x