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Beliebt Rechnen >

integral from 1 to 3 of xe^{-x^2}

Lösung

\int_{1}^{3} x e^{- x^{2}} d x

Lösung

\frac{e ^{8} - 1}{2 e ^{9}}

+1

Dezimale

0.18387 \dots

Schritte zur Lösung

\int_{1}^{3} x e^{- x^{2}} d x

Wende U-Substitution an

= \int_{- 1}^{- 9} - \frac{e ^{u}}{2} d u

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

= - \int_{- 9}^{- 1} - \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= - (- \frac{1}{2} \cdot \int_{- 9}^{- 1} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- \frac{1}{2} [e^{u}]_{- 9}^{- 1})

Vereinfache

= \frac{1}{2} [e^{u}]_{- 9}^{- 1}

Berechne die Grenzen:

\frac{1}{e} - \frac{1}{e ^{9}}

= \frac{1}{2} (\frac{1}{e} - \frac{1}{e ^{9}})

Vereinfache

= \frac{e ^{8} - 1}{2 e ^{9}}

Graph

Beliebte Beispiele

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steigung (0.2)(6.6)

s l o p e (0.2) (6.6)

limit as x approaches 3 of (x^2)/(9-x^2)

x \to 3 lim (\frac{x ^{2}}{9 - x ^{2}})

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\frac{d}{d x} (\frac{( e ^{x} )}{x ^{2}})

tangent 2/(x-1)

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