# An old IIT problem

Calculus Level 3

$\int_{\pi }^{2\pi} \lfloor 2 \sin x \rfloor \, dx$

If the value of the integral above is of the form $$\dfrac{A\pi }{B}$$, where $$A$$ and $$B$$ are coprime integers, find $$\left | A \right |+\left | B \right |$$.

Notations:

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