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Beliebt Rechnen >

integral from 1 to 2 of (e^{1/(x^3)})/(x^4)

Lösung

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{3}}}}{x ^{4}} d x

Lösung

\frac{e - 8 e}{3}

+1

Dezimale

0.52837 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{3}}}}{x ^{4}} d x

Wende U-Substitution an

= \int_{1}^{8} \frac{e ^{\frac{1}{u}}}{3 u ^{2}} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{1}^{8} \frac{e ^{\frac{1}{u}}}{u ^{2}} d u

Wende U-Substitution an

= \frac{1}{3} \cdot \int_{1}^{\frac{1}{8}} - e^{v} d v

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

= \frac{1}{3} (- \int_{\frac{1}{8}}^{1} - e^{v} d v)

Entferne die Konstante:

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

= \frac{1}{3} (- (- \int_{\frac{1}{8}}^{1} e^{v} d v))

Nutze das gemeinsame Integral :

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

= \frac{1}{3} (- (- [e^{v}]_{\frac{1}{8}}^{1}))

Vereinfache

= \frac{1}{3} [e^{v}]_{\frac{1}{8}}^{1}

Berechne die Grenzen:

e - 8 e

= \frac{1}{3} (e - 8 e)

Vereinfache

= \frac{e - 8 e}{3}

Graph

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