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Calculus Level 4

f(x)=limnx+2x+3x++nxn2\large f(x) = \lim_{n\to\infty} \dfrac{\lfloor x\rfloor+\lfloor 2x\rfloor+\lfloor 3x\rfloor+\cdots +\lfloor nx\rfloor}{n^2}

Let f(x)f(x) be defined as above and AA be the area bounded by f(x)f(x) and y=x2y=x^2. Then find 01/Af(x)dx\displaystyle\int_{0}^{1/A} f(x) \, dx.

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