integral from 0 to infinity of (1/2)^x

Lösung

\int_{0}^{\infty} (\frac{1}{2})^{x} d x

\frac{1}{ln ( 2 )}

Dezimale

1.44269 \dots

Schritte zur Lösung

\int_{0}^{\infty} (\frac{1}{2})^{x} d x

Berechne das unbestimmte Integral:

\int (\frac{1}{2})^{x} d x = - \frac{1}{ln ( 2 ) \cdot 2 ^{x}} + C

Berechne die Grenzen:

\int_{0}^{\infty} (\frac{1}{2})^{x} d x = 0 - (- \frac{1}{ln ( 2 )})

= 0 - (- \frac{1}{ln ( 2 )})

Vereinfache

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

\int_{- \infty}^{1} \frac{1}{x} d x

\int_{0}^{2} 1 - ∣ 1 - x ∣ d x

\int_{0}^{x} cos (x) sin (x) d x

\int_{0}^{2} (x^{2} + 8 x) d x

\int_{0}^{s} 1 d s