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Beliebt Rechnen >

integral from 0 to sqrt(t of)xe^{-x^2}

Lösung

\int_{0}^{t} x e^{- x^{2}} d x

Lösung

- \frac{1}{2} (e^{- t} - 1)

Schritte zur Lösung

\int_{0}^{t} x e^{- x^{2}} d x

Wende U-Substitution an

= \int_{0}^{- t} - \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_{0}^{- t} e^{u} d u

Nutze das gemeinsame Integral :

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

= - \frac{1}{2} [e^{u}]_{0}^{- t}

Berechne die Grenzen:

e^{- t} - 1

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

Beliebte Beispiele

((x^4)/8+1/(4x^2))^'

(\frac{x ^{4}}{8} + \frac{1}{4 x ^{2}})^{^{'}}

derivative of e^{(x^2/2}x)

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

integral of e^{-3y}

\int e^{- 3 y} d y

limit as x approaches 6 of x+6

x \to 6 lim (x + 6)

(d^2)/(dx^2)(1/(3+t))

\frac{d ^{2}}{d x ^{2}} (\frac{1}{3 + t})