If the area of the region S ={(x, y) : 2y - y 2 x 2 2y, x y} is equal to , then the natural num…

Question

If the area of the region S ={(x, y) : 2y - y 2  x 2  2y, x  y} is equal to  , then the natural number n is equal to_______

CGP EDU Academic Team · Accepted Answer

The correct answer is 5. (5)
Given,
S={(x,y) :2y-y 2  X 2  2y, X  y},
Now plotting the diagram, we get

Now from above diagram, given region are,
2y-y 2  x 2 ,x 2  2y and x  y
Now the intersecting point of x 2 + y 2 - 2y = 0 & x = y will be (1,1) and x 2 = 2y & x = y will be (2, 2)
So, required area will be,

So, on comparing we get, n = 5
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