• # question_answer Let $f:R\to R$ be a function and satisfies $f(2)=-1,f'(2)=4$. If $\int\limits_{2}^{3}{(3-x)f''(x)dx=7}$, then f[c] has the value equal to A)  10                                B)  9 C)  8                                 D)  5

$\int\limits_{2}^{3}{(3-x)\,f''(x)\,dx=7;}$ $\Rightarrow \,\,(3-x).\,f'(x)|_{2}^{3}\,+\int\limits_{2}^{3}{f'(x)\,dx=7}$ $\Rightarrow \,\,0-f'(2)+f(3)\,-f(2)=7$ $\Rightarrow \,\,-4+f(3)+1\,=7\Rightarrow \,f(3)=10$