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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{e - 1}{2}

+1

Dezimale

0.85914 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e - 1

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

Vereinfache

= \frac{e - 1}{2}

Graph

Beliebte Beispiele

integral from-2 to 2 of (x-5)

\int_{- 2}^{2} (x - 5) d x

integral from 5 to 10 of (6x)/(3x^2-5)

\int_{5}^{10} \frac{6 x}{3 x ^{2} - 5} d x

integral from-3 to-1 of x

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

integral from 4 to 9 of x^2

\int_{4}^{9} x^{2} d x

integral from-3 to 3 of 5

\int_{- 3}^{3} 5 d x