integral from 4 to sqrt(17 of)xe^{-x^2}

Lösung

\int_{4}^{17} x e^{- x^{2}} d x

\frac{e - 1}{2 e ^{17}}

Dezimale

3.55679 E - 8

Schritte zur Lösung

\int_{4}^{17} x e^{- x^{2}} d x

Wende U-Substitution an

= \int_{- 16}^{- 17} - \frac{e ^{u}}{2} d u

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

= - \int_{- 17}^{- 16} - \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_{- 17}^{- 16} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- \frac{1}{2} [e^{u}]_{- 17}^{- 16})

Vereinfache

= \frac{1}{2} [e^{u}]_{- 17}^{- 16}

Berechne die Grenzen:

\frac{1}{e ^{16}} - \frac{1}{e ^{17}}

= \frac{1}{2} (\frac{1}{e ^{16}} - \frac{1}{e ^{17}})

Vereinfache

= \frac{e - 1}{2 e ^{17}}

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