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 : (1) 11 (2) 13 (3) 15 (4) 9
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 :\\
(1) 11\\
(2) 13\\
(3) 15\\
(4) 9