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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{e - 1}{2}

+1

Dezimale

0.85914 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

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

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

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

Berechne die Grenzen:

e - 1

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

Vereinfache

= \frac{e - 1}{2}

Graph

Beliebte Beispiele

(3sqrt(x-1)+4sqrt(5-x))^'

(3 x - 1 + 4 5 - x)^{^{'}}

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\int \frac{1}{5 x} d x

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\int 16 - x^{2} x d x

integral from 0 to 3 of (3-x)^2

\int_{0}^{3} (3 - x)^{2} d x

y^{''}+5y^'+4y=8te^{2t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 t e^{2 t}