1.
f:[0,1][0,1]f:[0,1]\to[0,1] continuous, x2+f(x)21x^2+f(x)^2\le1, 01f=π/4\int_0^1 f = \pi/4. Then 1/21/2f(x)1x2dx\int_{1/2}^{1/\sqrt2}\frac{f(x)}{1-x^2}dx equals