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Beliebt Rechnen >

integral from 0 to 1 of x^3e^{-x^2}

Lösung

\int_{0}^{1} x^{3} e^{- x^{2}} d x

Lösung

- \frac{- e + 2}{2 e}

+1

Dezimale

0.13212 \dots

Schritte zur Lösung

\int_{0}^{1} x^{3} e^{- x^{2}} d x

Wende U-Substitution an

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

- 1 + \frac{2}{e}

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

Vereinfache

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

Graph

Beliebte Beispiele

limit as x approaches c of x^2+a

x \to c lim (x^{2} + a)

derivative 1/(\sqrt[8]{x)}

d er i v a t i v e \frac{1}{8 x}

integral of (3x+5)e^{(3x+5)}

\int (3 x + 5) e^{(3 x + 5)} d x

derivative y=2e^x+8/(\sqrt[3]{x)}

d er i v a t i v e y = 2 e^{x} + \frac{8}{3 x}

(dP)/(dt)=5sqrt(Pt)

\frac{d P}{d t} = 5 Pt