Intergrate

hi, i've been working on the following question below and would like any help whatsoever….for the circuit shown below, assuming zero charge on the capacitor at t = 0, the current flowing may be quantified as: i=e/r * e^-t/rc integrate this equation with respect to t and hence find the charge stored in the capacitor 0.5 seconds after the switch is closed.

No not intergrated exponential and wasn’t sure how to start my working out

I have done some work on this but I don’t think it’s correct

I can differentiate but never tried “reverse it”. I’m just working from a work book which is the only info I have. Hence I’m stuck

A quick google gave many hits so things like
https://www.youtube.com/watch?v=MTL1yTVtNMQ&ab_channel=ExamSolutions
In your case, the b in the exponent is zero and the a=...

Ok so where would you start with my equation? I over think everything and tie myself in knots

From the video you should be able to integrate things like
e^(-t)
E e^(-t)
(E/R) e^(-t)
(E/R) e^(-t/(RC))
so try and do simpler ones first and check by differentiating your answer and make sure you get the original function. Post what youve done for these, or similar ones that you choose.

e^(-t) dt = e^(-t) + C

-e^(-t)+C

E(-e^-t)+C