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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{8}{9 ln ( 3 )}

+1

Dezimale

0.80910 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{0}^{- 2} - 3^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 2}^{0} - 3^{u} d u

Entferne die Konstante:

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

= - (- \int_{- 2}^{0} 3^{u} d u)

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - (- [\frac{3 ^{u}}{ln ( 3 )}]_{- 2}^{0})

Vereinfache

= [\frac{3 ^{u}}{ln ( 3 )}]_{- 2}^{0}

Berechne die Grenzen:

\frac{8}{9 ln ( 3 )}

= \frac{8}{9 ln ( 3 )}

Graph

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