A Nice Geometry Problem (1)

Calculus Level 4

A circle of radius 1 is tangent to the parabola \(y=x^2,\) as shown.

Find the gray area between the circle and the parabola.

If the area can be written as \(\dfrac{A\sqrt{A}}{B}-\dfrac{\pi}{A},\) then what is \(A+B?\)

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