The figure shows region $A$, which is bounded by the $x$- and $y$-axes, and the graph of $f(x)=\dfrac{sinx}{x}$, for $x>0$, and the vertical line $x=k$. If $k$ increases at a rate of $\pi/4$ units per second, how fast is the area of region $A$ changing when $k=\pi/6$?
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