Assume the charge at the upper terminal is zero at the instant the current is passing through its maximum value. find the expression for q(t).
i = 24cos4000t A

im not sure if i taken the correct integral of it. i got q(t) = (24cos4000t)1/2t^2

also for the same question but when i=0 when t<0 and i=20e^-5000tA when t> or equal to 0.

 

Hmm, the integral of cos is sin. So the final function should have a sin in it. And also when you integrate cos(kt) where k is a constant you get sin(kt) divided by the stuff inside the cos function differentiated. That is

sin(kt) / k.

Try integrating again with this in mind.