Why Does Integrating Current Over Time Equal the Initial Charge of a Capacitor?

[Puchinita5]

Homework Statement

Hi. I had to do a lab on charging and discharging capacitors. In my lab packet, my professor asks:
"We know by definition I=dq/dt. So if we calculate the integral Idt (from zero to infinity) = integral dq (from zero to infinity) it should be equal to q(0) (the initial charge of the capacitor). Explain briefly (show some steps in your derivation) why this is the case.

i'm not 100% sure if I'm understanding the question right. But i'll show my attempt

Homework Equations

The Attempt at a Solution

q(t)=Qe^(-t/RC) where Q is the max charge.

so the integral of dq from zero to infinity should be q(infinity)-q(0)...

and since q(infinity) approaches zero, i'll assume it just equals zero...

my problem is, this leaves me with -q(0)...i don't know if the negative sign makes a huge difference in what he's asking, but i feel like it does? Anyone have a clue?

 

[rl.bhat]

Limit of dq cannot be from zero to infinity but the the limit of time can be zero to infinity. It should be zero to qo.