Let A = [1, 3, -1; 2, 1, α; 0, 1, -1] be a singular matrix. Let f(x)=∫_0^x( t^2+2 t +3) dt, x ∈[1, α]. If M and m are respectively the maximum and…

Let $\displaystyle \mathrm{A}=\left[\begin{array}{ccc}1 & 3 & -1 \\ 2 & 1 & \alpha \\ 0 & 1 & -1\end{array}\right]$ be a singular matrix. Let $\displaystyle f(x)=\int_0^x\left(\mathrm{t}^2+2 \mathrm{t}+3\right) \mathrm{dt}, x \in[1, \alpha]$. If M and m are respectively the maximum and the minimum values of $\displaystyle f$ in $\displaystyle [1, \alpha]$, then $\displaystyle 3(\mathrm{M}-\mathrm{m})$ is equal to :