# Is the integral actually zero?

Calculus Level 5

The following shown here is a portion of the graph for $$f\left( x \right) =\sqrt { 1-\tan ^{ 2 }{ x } }$$, in which all regions bound by the $$x$$-axis and $$f\left( x \right)$$ are shaded.

Considering the periodic properties of $$f\left( x \right)$$, the area of any shaded region can be expressed in the form $$\pi \tan { \frac { \pi }{ A } }$$, with $${ A }$$ being a positive, root-free integer. Find $${ A }$$.

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