The change following through a resistance R varies with time ‘t’ as Q = at - bt2 . The total heat produced in R is

Q = at - bt2 ⇒i=dQdt=a - 2bt now, i = 0  at  t = a2b Total heat produced is given by H=∫0a/2bi2Rdt=R∫0a/2ba−2bt2dt   =R∫0a/2ba2−4abt+4b2t2 dt =Ra2t−4abt22+4b2t330a/2b =Ra2.a2b−4ab2.a24b2+4b23.a38b3 =a3Rb12−12+16=a3R6b