Let the area enclosed by the lines x + y = 2 , y = 0 , x = 0 and the curve f ( x ) = min { x 2 + 3 4 , ? 1 + [ x ] } , where [ x ] denotes the greatest integer x , be A . Then the value of 12 A is [2023]

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Solution

Q.
Let the area enclosed by the lines $x + y = 2, y = 0, x = 0$ and the curve $f (x) = \min {x^{2} + \frac{3}{4}, 1 + [x]},$ where $[x]$ denotes the greatest integer $\leq x$ , be $A$ . Then the value of $12 A$ is____________ . [2023]

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