# Finding the intergral function (dQ/dt) = kQ

1. Apr 27, 2012

1. The problem statement, all variables and given/known data
Find the integral (I think I'm finding the integral) of:
$\frac{dQ}{dt}$ =kQ

2. Relevant equations

3. The attempt at a solution
I just got feedback from my teacher, and he told me I make a mistake somewhere in this question. But I don't know where I've gone wrong?

$\frac{dQ}{dt}$=kQ
$\frac{dQ}{Q}$=kdt
∫$\frac{dQ}{Q}$=∫kdt
lnQ=kt+c
Q=ekt+ec
Where ec is a constant, so let ec=A
Q=Aekt

∴ Q=Aekt

Can anyone see where I've gone wrong?

Last edited: Apr 27, 2012
2. Apr 27, 2012

### spaghetti3451

If you substitute your solution back into the differential equation, the LHS equals the RHS, so the solution is fine. However, you wrote in an intermediate calculation that Q = ekt + ec. It can't be an addition. Try and think why it can't be an addition.

Hint: What are rules for algebraic operations with indices?

3. Apr 27, 2012

oh... Kt + c will have to go to

ekt+c
ektx ec

right?

4. Apr 27, 2012

### spaghetti3451

Yup, I can't see any other mistakes. This answer should score full marks now.

5. Apr 27, 2012

awesome!

Thanks man, I owe you one

6. Apr 27, 2012

### HallsofIvy

Staff Emeritus
Technically, there is one other error. The integral, $\int (1/Q)dQ= ln|Q|$, not ln(Q).

7. Apr 28, 2012

ahhh... ok, thanks for that

8. Apr 28, 2012

### Staff: Mentor

Minor point: there is no such word as "intergral" in the English language. Seeing as you have started two threads with this in the title, I thought I should point it out.

9. Apr 28, 2012