Let \( y=f(x) \) and \( y=g(x) \) be the pair of curves such that (i) the tangents at point with...

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Let \( y=f(x) \) and \( y=g(x) \) be the pair of curves such that
(i) the tangents at point with equal abscissa intersect on \( y \)-axis
(ii) the normals drawn at points with equal abscissa intersect on \( x \)-axis and
(iii) the curve \( f(x) \) passes through \( (1,1) \) and \( g(y) \) passes through \( (2,3) \) then
The value of \( \int_{1}^{2}(g(x)-f(x)) d x \) is
(a) 2
(b) 3
(c) 4
(d) \( 4 \ln 2 \)
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