Nested stuff

Calculus Level 3

\[ \large y = \int_{-1}^{1} \left ( \sqrt{ 1 - \sqrt {1 - \sqrt{ 1 -\dots \sqrt{1 - x^2}}}} \right) \text{d}x \, \]

Consider the nested function above, what is the value of \(y\) in the limit of infinite nesting? Give your answer to 3 decimal places.

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