In an electronics laboratory, the current in a circuit at time t seconds is modelled by i(t)=te−0.5t amperes.
a. Write an expression for the total charge Q(t) (in coulombs) that has passed through the circuit up to time t seconds in terms of an indefinite integral of i(t).
b. Evaluate the integral obtained in part (i), expressing Q(t) in its simplest form and including the constant of integration.