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Beliebt Rechnen >

integral from 1 to sqrt(2 of)xe^{x^2}

Lösung

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

Lösung

\frac{e ^{2} - e}{2}

+1

Dezimale

2.33538 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{2} \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}^{2} e^{u} d u

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e^{2} - e

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

Vereinfache

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

Graph

Beliebte Beispiele

integral of-2tan(2y)

\int - 2 tan (2 y) d y

fläche 12-x^2,x^2-6,[-3,3]

a re a 12 - x^{2}, x^{2} - 6, [- 3, 3]

tangent y= 1/x ,(2, 1/2)

t an g e n t y = \frac{1}{x}, (2, \frac{1}{2})

(\partial)/(\partial x)(e^{sin(x)})

\frac{\partial}{\partial x} (e^{s i n (x)})

derivative of sqrt(16-x)

\frac{d}{d x} (16 - x)