Find the area in the first quadrant bounded by

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

Problem

[x] + [y] = n

, where

n \in \mathbb{N}

and

y = i

(where,

i \in \mathbb{N} \forall i \le n+1

[ \cdot ]

denotes the greatest integer less than or equal to

x