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

Lösung

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

e - e

Dezimale

1.06956 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{\frac{1}{2}} - e^{u} d u

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

= - \int_{\frac{1}{2}}^{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}{2}}^{1} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- [e^{u}]_{\frac{1}{2}}^{1})

Vereinfache

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

Berechne die Grenzen:

e - e

= e - e

f a c t or 2 cos (x) + cos^{2} (x)

y^{^{''}} + 3 y^{^{'}} + 2 y = 6

a re a f (x) = cos (x), 0, 2 π

\int \frac{3 cos ( x )}{sin ^{2} ( x ) + sin ( x )} d x

n = 3 \sum \infty \frac{n}{e ^{3 n}}