Question

$\stackrel{\infty }{\underset{0}{\int }}(a^{-x}-b^{-x})dx$ equals-

• A. $\frac{1}{\log a}-\frac{1}{\log b}$
• B. $\log a-\log b$
• C. $\log a+\log b$
• D. $0$

Answer 1

Answer: (A)

$\frac{1}{\log a}-\frac{1}{\log b}$

Now,

$\stackrel{\infty }{\underset{0}{\int }}(a^{-x}-b^{-x})dx$

$={\left[\frac{-a^{-x}}{\log a}\right]}_{x=0}^{x=\infty }$$+{\left[\frac{b^{-x}}{\log b}\right]}_{x=0}^{x=\infty }$

$=\frac{1}{\log a}-\frac{1}{\log b}$