In an electronics laboratory

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

In an electronics laboratory, the current in a circuit at time

t

seconds is modelled by

i(t)=t\,e^{-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.