The voltage pulse described by the following equations is impressed across the terminals of a 0.5µF capacitor. v(t) = 0 t ≤ 0 v(t) = 4t V 0 ≤ t ≤ 1 v(t) = 4e-(t-1) V 1 ≤ t ≤ [infinity] a. Derive the expressions for the capacitor current, power, and energy. b. Sketch the voltage, current, power, and energy as functions of time. Line the plots up vertically so that for a given time interval the behavior of each variable can easily be assessed. c. Specify the interval of time when energy is being stored in the capacitor. d. Evaluate the integral ∫ from (i) t = 0 to 1 and (ii) t = 1 to [infinity]; comment on the significance of these two integrals