Explanation

(b)
$\therefore$ Area $= \int_{2}^{4}{\left( 1 + \frac{8}{x^{2}} \right)dx}$
Since, the ordinate $x = a$ divides area into two equal parts, therefore,
$\int_{2}^{a}{\left( 1 + \frac{8}{x^{2}} \right)dx = \frac{1}{2}\int_{2}^{4}{\left( 1 + \frac{8}{x^{2}} \right)dx}}$
$\Rightarrow \ \left\lbrack x - \frac{8}{x} \right\rbrack_{2}^{a} = \frac{1}{2}\left\lbrack x - \frac{8}{x} \right\rbrack_{2}^{4}$
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$\Rightarrow \ \left( a - \frac{8}{a} \right) - (2 - 4) = \frac{1}{2}\left\lbrack (4 - 2) - (2 - 4) \right\rbrack$
$\Rightarrow \ a - \frac{8}{a} + 2 = 2$
$\Rightarrow \ a = \sqrt{8} = 2\sqrt{2}\ sq\ unit$