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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{e - 1}{e}

+1

Dezimale

0.23865 \dots

Schritte zur Lösung

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

e^{x - 1} = e^{- 1} e^{x}

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

a^{- 1} = \frac{1}{a}

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e - 1

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

Vereinfache

= \frac{e - 1}{e}

Graph

Beliebte Beispiele

integral from-1 to 3 of (x^2-1)

\int_{- 1}^{3} (x^{2} - 1) d x

integral from-6 to 4 of x-1

\int_{- 6}^{4} x - 1 d x

integral from-4 to 5 of |2x|

\int_{- 4}^{5} ∣ 2 x ∣ d x

integral from 0 to 5 of x-5

\int_{0}^{5} x - 5 d x

integral from x^2 to x^4 of sqrt(t)

\int_{x^{2}}^{x^{4}} t d t