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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{e - 1}{3 e}

+1

Dezimale

0.21070 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{- 1}^{0} \frac{e ^{u}}{3} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{- 1}^{0} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [e^{u}]_{- 1}^{0}

Berechne die Grenzen:

1 - \frac{1}{e}

= \frac{1}{3} (1 - \frac{1}{e})

Vereinfache

= \frac{e - 1}{3 e}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(x^2+y^3+w^4)

\frac{\partial}{\partial x} (x^{2} + y^{3} + w^{4})

fläche y=|3x|,y=x^2-4

a re a y = ∣ 3 x ∣, y = x^{2} - 4

integral of 1/(1-4x)

\int \frac{1}{1 - 4 x} d x

limit as x approaches-1 of (x^2+5)/(x+6)

x \to - 1 lim (\frac{x ^{2} + 5}{x + 6})

derivative (2x+3)^{1.4}

d er i v a t i v e (2 x + 3)^{1.4}