A Bit Tricky

Calculus Level 5

\[f(a,b) = \int_{b}^{a}\dfrac{x^2 \, dx}{\sqrt{1-x^2}}\]\[g(a,b) = \int_{a}^{b}\dfrac{x^2 \, dx}{\sqrt{1-x^2}-1}\] If \(a^2-b^2 = 1\), find the value of \[\left \lfloor \max((f+g)(a,b)) \right \rfloor- \left \lfloor \min((f+g)(a,b)) \right \rfloor \; . \]

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