Explanation

(b)
$Area\ of\ curve\ MNBA = \int_{2}^{4}{\left( 1 + \frac{8}{x^{2}} \right)dx}$
$= \left\lbrack x - \frac{8}{x} \right\rbrack_{2}^{- 4} = 4\ \ \ldots.(i)$
[image:8_image12.jpeg]
$Area\ of\ curve\ ACDM = \int_{2}^{a}{\left( 1 + \frac{8}{x^{2}} \right)dx}$
$= \left\lbrack x - \frac{8}{x} \right\rbrack_{2}^{a} = a - \frac{8}{a} - \lbrack 2 - 4\rbrack = a - \frac{8}{a} + 2\ \ \ldots.(ii)$
Form Eqs. (i) and (ii), we get
$a - \frac{8}{a} + 2 = \frac{1}{4}(4)$
$\Longrightarrow \ \ a^{2} - 8 = 0\ \ \Longrightarrow a = 2\sqrt{2}\ \ \ \ \ \lbrack\because a > 0\rbrack$