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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{4 ln ( 2 )}

+1

Dezimale

0.36067 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{- 1}^{- 2} - 2^{u} d u

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

= - \int_{- 2}^{- 1} - 2^{u} d u

Entferne die Konstante:

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

= - (- \int_{- 2}^{- 1} 2^{u} d u)

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

= - (- [\frac{2 ^{u}}{ln ( 2 )}]_{- 2}^{- 1})

Vereinfache

= [\frac{2 ^{u}}{ln ( 2 )}]_{- 2}^{- 1}

Berechne die Grenzen:

\frac{1}{4 ln ( 2 )}

= \frac{1}{4 ln ( 2 )}

Graph

Beliebte Beispiele

integral from 0 to 1 of (25)/(4y-1)

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x \to 0 + lim (x ln (x + x^{2}))

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