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Calculus Level 5

Find the area of the region bounded by the x-axis and the curves defined by $\begin{cases} y=tanx, ~~~ \frac{-\pi}{3} \leq x \leq \frac{\pi}{3} \\ y=cotx, ~~~ \frac{\pi}{6} \leq x \leq \frac{3.\pi}{2} \end{cases}$ If your answer comes out to be $$log(\lambda)$$, then find the value of $\lceil \frac{1}{\lambda} \rceil$

Note : $$\lceil .. \rceil$$ denotes the Ceiling Function (Lowest integer greater than equal to).

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