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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{e ^{7} - 1}{3}

+1

Dezimale

365.21105 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{7} \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_{0}^{7} e^{u} d u

Nutze das gemeinsame Integral :

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

= \frac{1}{3} [e^{u}]_{0}^{7}

Berechne die Grenzen:

e^{7} - 1

= \frac{1}{3} (e^{7} - 1)

Vereinfache

= \frac{e ^{7} - 1}{3}

Graph

Beliebte Beispiele

sum from n=1 to infinity of 1/(\sqrt[n]{2)}

n = 1 \sum \infty \frac{1}{n 2}

y^{''}+9y=(sec(3t))^2

y^{^{''}} + 9 y = (sec (3 t))^{2}

(dy}{dx}+(2y)/x =\frac{sin(x))/(x^2)

\frac{d y}{d x} + \frac{2 y}{x} = \frac{sin ( x )}{x ^{2}}

laplacetransform te^{-t}

l a pl a ce t r an s f or m t e^{- t}

derivative of e^{-2x}-3y

\frac{d}{d x} (e^{- 2 x} - 3 y)