Calculate Energy Applied to Steel Slab

[debo22]

I want to calculate the energy applied to a slab of steel with a temperature rise that varying with time (t) as -
13t + 5t^2 + 10* sin (3ωt)

The energy applied to the system is calculated by mc (dT) equation where
m mass of the slab
c specific heat
dT change in temperature

 

[HallsofIvy]

Are m and c constant?

Then $dt= 13+ 10t+ 30\omega cos(3\omega t)$, of course.