Alternating signs

Calculus Level 5

y=xx+xx+ \displaystyle y= \sqrt{x-\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{\cdots}}}}}

Given that 1.754.75ydx=ab\displaystyle \int_{1.75}^{4.75} y \,dx = \frac{a}{b}, where aa and bb are coprime positive integers, find a+ba+b.


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