# Area of a Region

Calculus Level pending

Let line $${\bf L}$$ be the tangent line to the curves $${\bf f(x) = -x^2 }$$ and $${\bf g(x) = \sqrt{x}. }$$

The area bounded by line $${\bf L }$$ and the two curves $${\bf f(x) = -x^2 }$$ and $${\bf g(x) = \sqrt{x} }$$ can be represented as $${\bf \frac{m}{n}, }$$ where $${\bf m }$$ and $${\bf n }$$ are coprime positive integers.

Find $${\bf m + n .}$$

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