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Beliebt Rechnen >

integral from 0 to 4 of xe^{x^2}

Lösung

\int_{0}^{4} x e^{x^{2}} d x

Lösung

\frac{e ^{16} - 1}{2}

+1

Dezimale

4443054.76025 \dots

Schritte zur Lösung

\int_{0}^{4} x e^{x^{2}} d x

Wende U-Substitution an

= \int_{0}^{16} \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}^{16} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{2} [e^{u}]_{0}^{16}

Berechne die Grenzen:

e^{16} - 1

= \frac{1}{2} (e^{16} - 1)

Vereinfache

= \frac{e ^{16} - 1}{2}

Graph

Beliebte Beispiele

integral from 0 to a of xsqrt(x^2+a^2)

\int_{0}^{a} x x^{2} + a^{2} d x

derivative of sin(2(x))

\frac{d}{d x} (sin (2) (x))

derivative-y/(x+e^y)

d er i v a t i v e - \frac{y}{x + e ^{y}}

integral from 0 to 3 of (6t)/((t-4)^2)

\int_{0}^{3} \frac{6 t}{( t - 4 ) ^{2}} d t

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

\int \frac{2 x e ^{x}}{( x + 1 ) ^{2}} d x