JEE-Advanced 2015 (6/40)

Calculus Level 4

Let f:RRf:\mathbb{R} \to \mathbb{R} be a function defined by f(x)={x  ,x20  ,x>2f(x)=\begin{cases} \lfloor x \rfloor \ \ , \quad x \leq 2 \\ 0 \ \ , \quad x>2 \end{cases} If I=12xf(x2)2+f(x+1)dxI=\displaystyle \int_{-1}^2 \frac{xf(x^2)}{2+f(x+1)}\, dx, then find the value of 4I14I-1.

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