A continuous function f:R→R satisfies the differential equation f(x)=(1+x2)⎛⎜⎝1+x∫0f2(t)1+t2 dt⎞⎟⎠. If area of triangle formed by tangent drawn to the curve y=f(x) at x=1 with the co-ordinates axis is △, then the value of [△3] is [Note: [K] denotes the greatest integer less than or equal to K.]

A continuous function f:R→R satisfies the differential equation f(x)

1.	A continuous function f:R→R satisfies the differential equation f(x)=(1+x2)⎛⎜⎝1+x∫0f2(t)1+t2 dt⎞⎟⎠. If area of triangle formed by tangent drawn to the curve y=f(x) at x=1 with the co-ordinates axis is △, then the value of [△3] is [Note: [K] denotes the greatest integer less than or equal to K.]
Answer» A continuous function $f : R \to R$ satisfies the differential equation $f (x) = (1 + x^{2}) ⎛ ⎜ ⎝ 1 + x \int 0 \frac{f^{2} (t)}{1 + t^{2}} d t ⎞ ⎟ ⎠ .$ If area of triangle formed by tangent drawn to the curve $y = f (x)$ at $x = 1$ with the co-ordinates axis is $△,$ then the value of $[\frac{△}{3}]$ is [Note: [K] denotes the greatest integer less than or equal to $K$ .]