Mathematics

Problem

Consider two curves

y = \frac{1}{x^2}

and

y = \frac{1}{4(x-1)}

. 'a' is a number such that

a > 2

& the reciprocal of the area of the figure bounded by the curves, the line

x = 2

x = a

a

itself. 'b' is a number such that

1 < b < 2

& the area bounded by the two curves & the lines

x = b

x = 2

is equal to

1 - \frac{1}{b}

. On the basis of above information, answer the following questions: The value of

\ln a - \ln b

is - (A) positive integer (B) negative integer (C) rational number of the form

\frac{p}{q}

, where

p, q

are co-prime &

q > 1

. (D) irrational number