Let be a singular matrix. Let \( f(x)=\int_{0}^{x}(t^{2}+2t+3)\,dt, \; x\in [\,1,\alpha\,] \). If \( M \) and \( m \) are respectively the maximum and the minimum values of \( f \) in \( [\,1,\alpha\,] \), then \( 3(M-m) \) is equal to:
\( 64 \)
\( 68 \)
\( 72 \)
\( 76 \)
be a singular matrix. Let \( f(x)=\int_{0}^{x}(t^{2}+2t+3)\,dt, \; x\in [\,1,\alpha\,] \). If \( M \) and \( m \) are respectively the maximum and the minimum values of \( f \) in \( [\,1,\alpha\,] \), then \( 3(M-m) \) is equal to: