# 5 years back

Calculus Level 5

$\large \displaystyle\int \dfrac{\sec^2(x) - 2010}{\sin^{2010}(x)}\, dx = \dfrac{P(x)}{(\sin(x))^{2010}} + C$

If the equation above is true for some function $$P(x)$$ with $$P ( \frac{ \pi}{4} ) = \frac{1}{2^{1005} }$$, where $$C$$ denotes the arbitrary constant, then find the value of $$P\left(\dfrac{\pi}{3}\right)$$.

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