A Nice Geometry Problem (1)

Calculus Level 3

A circle of radius 1 is tangent to the parabola y=x2,y=x^2, as shown.

Find the gray area between the circle and the parabola.

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

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