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Let $f (x) = \min {x - [x], 1 - x + [x]}, g (x) = \max {x - [x], 1 - x + [x]}$
(where [.] denotes G.I.F). The value of positive integer n, for which $\int_{0}^{n} (g (x) - f (x)) d x = 100$ is _____

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100

200

198

202

answer is B.

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Detailed Solution

$[\int_{0}^{n} (g (x) - f (x)) d x = n \int_{0}^{1} (g (x) - f (x)) d x$

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