Explanation:
As, \(I = \frac{{dq}}{{dt}}\)
\( \Rightarrow \int d q = \int_{{t_1}}^{{t_2}} I dt\)
\(\therefore \;\;\;{\mkern 1mu} {\kern 1pt} \,\,\,\,\,q = \int_0^2 {\left[ {3{t^2} + 2t + 5} \right]} dt\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{3}{3}\left[ {{t^3}} \right]_0^2 + \frac{2}{2}\left[ {{t^2}} \right]_0^2 + 5[t]_0^2\)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 8 + 4 + 10 = 22C\)