[Solved] Let F(x) = \\int_{x}^{x^2 + \\frac{\\pi}{6}} 2 \\cos^2t dt for all x \\in R and f : \\left[0, \\frac{1}{2}\\right] \\rightarrow [0, \\infty) be a continuous function. For a \\in \\left[0, \\frac{1}{2}\\right], if F' (a) + 2 is the area of the region bounded by x = 0, y = 0, y = f(x) and x = a, then f(0) is - - JEE (Advanced) 2015 Paper-1