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Beliebt Rechnen >

integral from 0 to 1 of xe^{-x^2}

Lösung

\int_{0}^{1} x e^{- x^{2}} d x

Lösung

\frac{e - 1}{2 e}

+1

Dezimale

0.31606 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{- x^{2}} d x

Wende U-Substitution an

= \int_{0}^{- 1} - \frac{e ^{u}}{2} d u

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

= - \int_{- 1}^{0} - \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_{- 1}^{0} e^{u} d u)

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

Berechne die Grenzen:

1 - \frac{1}{e}

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

Vereinfache

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

Graph

Beliebte Beispiele

integral of-1/(1+x^2)

\int - \frac{1}{1 + x ^{2}} d x

integral of sin(-1(x))

\int sin (- 1 (x)) d x

limit as x approaches 0-of (sec(x))/x

x \to 0 - lim (\frac{sec ( x )}{x})

y^{''}+6y^'+6y=0,y(0)=1,y^'(0)=2

y^{^{''}} + 6 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 2

derivative of (x-1^2+y^2)

\frac{d}{d x} ((x - 1)^{2} + y^{2})