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

Lösung

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

\frac{e - 1}{2}

Dezimale

0.85914 \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

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}

Berechne die Grenzen:

e - 1

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

Vereinfache

= \frac{e - 1}{2}

\int_{0}^{1} (2 x^{2} - 1) d x

(sin (x) - y sin (x) - 2 cos (x)) + cos (x) y^{^{'}} = 0

\frac{d}{d x} (\frac{e ^{4 x}}{ln ( 6 x )})

\int \frac{2 x}{e ^{x}} d x

\frac{d}{d x} (36 x^{2})