Let f:[0,1]rarr[0,1] be a continuous fun...

Let `f:[0,1]rarr[0,1]` be a continuous function such that `x^2+(f(x))^2le1` for all `x in [0,1]` and `int_0^1f(x)dx=pi/4`. Then`int_(1/2)^(1/sqrt2)f(x)/(1-x^2)dx` equals

`pi/12`

`pi/15`

`(sqrt2-1)/2pi`

`pi/10`

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