Let denotes the greatest integer function

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let [x][x] denotes the greatest integer function. Draw a rough sketch of the portions of the curves x2=4[x]y and y2=4[y]x that lie within the square {(x,y)∣1≤x≤4,1≤y≤4}.x^2 = 4[\sqrt{x}]y \text{ and } y^2 = 4[\sqrt{y}]x \text{ that lie within the square } \{(x, y) \mid 1 \le x \le 4, 1 \le y \le 4\}. Find the area of the part of the square that is enclosed by the two curves and the line x+y=3x + y = 3.

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