Area bounded by the relation [2x]+[y]=5,x,y>0is ____( where [.] represents greatest integer function

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Area bounded by the relation $[2 x] + [y] = 5, x, y > 0$ is ____

( where [.] represents greatest integer function

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answer is 3.

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Detailed Solution

$[2 x] = 0 \Rightarrow 2 x \in [0, 1)$ $\Rightarrow \in [0, \frac{1}{2}) \Rightarrow [y] = 5 \Rightarrow y \in [5, 6)$

Similarly we can consider [2x] = 1,2,3,4 and 5

From the graph, area is 3sq. units

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