Explanation

(b) The instantaneous power is the limiting value of the average power as the time interval $\mathrm{\Delta}\ t$ approaches zero.
$P = \lim_{\mathrm{\Delta}t \rightarrow 0}\frac{\mathrm{\Delta}W}{\mathrm{\Delta}t}\ \ \ $
$\therefore\ W = \int_{}^{}{P\ dt}$
Given $P = 3t^{2} - 2t + 1$
$\therefore\ W = \int_{2}^{4}{(3t^{2} - 2t + 1)}dt$
$W = \left\lbrack t^{3} - t^{2} + t \right\rbrack_{2}^{4} = 56 - 12 + 2$
$\Longrightarrow \ \ \ \ \ \ W = 46\ J$