$\int\limits_0^{\infty}\left(a^{-x}-b^{-x}\right) d x=$
Answer & explanation
Correct answer: option 1
$=\int\left(a^{-x}-b^{-x}\right) d x=\left[\frac{a^{-x}}{-\log a}-\frac{b^{-x}}{-\log b}\right]_0^{\infty}=0+\frac{a^0}{\log a}-\frac{b^0}{\log b}=\frac{1}{\log a}-\frac{1}{\log b}$
Hence (1) is the correct answer.