The current in a conductor varies with time t as $I = 2t + 3{t^2}$ where $I$ is in ampere and $t$ in seconds. Electric charge flowing through a section of the conductor during $t = 2\,\sec$ to $t = 3\,\sec$ is ............. $C$
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$dQ = Idt$
$\Rightarrow $ $Q = \int_{t = 2}^{t = 3} {\,Idt} = $ $\left[ {2\int\limits_2^3 {tdt} + 3\int\limits_2^3 {{t^2}dt} } \right]$
$= \left[ {{t^2}} \right]_2^3 + \left[ {{t^3}} \right]_2^3= (9 -4) + (27 -8) = 5 + 19 = 24\,C$.
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