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The area bounded by the curves $y = 2 x^{2}, y = \max {x - [x] + | x |}$ and the lines $x = 0, x = 2$ (in sq.units), is

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$\frac{1}{2}$

$\frac{1}{3}$

$\frac{4}{3}$

answer is A.

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Detailed Solution

$y = 2 x^{2}$
$y = \max {x = [x], x + | x |} = x + | x |$
Required area $= \int_{0}^{1} (2 x - x^{2}) d x + \int_{1}^{2} (2 x^{2} - 2 x) d x$

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