Alternating signs

Calculus Level 5

\[ \displaystyle y= \sqrt{x-\sqrt{x+\sqrt{x-\sqrt{x+\sqrt{\cdots}}}}} \]

Given that \(\displaystyle \int_{1.75}^{4.75} y \,dx = \frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).


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