Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) be a twice differentiable function such that \(f(2)=1\). If \(\mat…

Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) be a twice differentiable function such that \(f(2)=1\). If \(\mathrm{F}(x)=x f(x)\) for all \(x \in \mathbf{R}\), \(\int_0^2 x \mathrm{~F}^{\prime}(x) \mathrm{d} x=6\) and \(\int_0^2 x^2 \mathrm{~F}^{\prime \prime}(x) \mathrm{d} x=40\), then \(\mathrm{F}^{\prime}(2)+\int_0^2 \mathrm{~F}(x) \mathrm{d} x\) is equal to :

[JEE Main 2025, 28 Jan (Shift 2)]