# Its Area

Calculus Level 5

The area of the region bounded by the circle $$(x-1)^{2}+y^{2}=6$$ and the curve given by $$f\left( x \right) =\left| \begin{matrix} 1-x & x-1 & 1 \\ x-2 & -x & 2x-{ x }^{ 2 } \\ x+1 & 3-x & { 2x }^{ 2 }-4x \end{matrix} \right|$$ lying above the curve is

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