# Will you integrate?(1)

Calculus Level 4

Let $${A}_{1}$$ be the area of polygon with vertices $$P (x,y)$$ such that $$\left\lfloor \left| x \right| \right\rfloor +\left\lfloor \left| y \right| \right\rfloor =n$$; and $${A}_{2}$$ be the area bounded by the curve $$\left| x \right| +\left| y \right| =n+1$$. Find value of $$n$$ such that $$\left|{A}_{1}-{A}_{2}\right|=96 \text{ unit}^2$$.

Bonus: Generalize for all positive integers $$n$$.

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