# Integration problem

• Jun 1st 2008, 05:06 PM
thecakeisalie
Integration problem
Hey everyone. This has been really bugging me for 4 hours now, and I cannot figure out where I am going wrong. If anyone can help me that would be greatly appreciated.

The current flowing through a capacitor is:

I = Ioe^-(kt)

Io = 2 amps
k = 0.2s
T = time

Find the charge flowed after the first 5 seconds

Q = I dt

2e^-(0.2t) dt

= 1/-0.2e^-(0.2t)

= -10e^-(0.2t)

5
| -10e^-(0.2t)
0

[ -10e^-(0.2t)] = {-10e^-(0.2x5)} - {-10e^-(0.2x0)}

= -10e^-1 - 0

Then I end up with a negative number for Q . If anyone could point me in the right direction i'd be thankful .
• Jun 1st 2008, 06:40 PM
TheEmptySet
Quote:

5
| -10e^-(0.2t)
0

[ -10e^-(0.2t)] = {-10e^-(0.2x5)} - {-10e^-(0.2x0)}

= -10e^-1 - 0

Then I end up with a negative number for Q . If anyone could point me in the right direction i'd be thankful .
$e^0=1 \ne 0$
$-10e^{-0.2t} \bigg|_{0}^{5}=-10e^{-1}-[-10e^{0}]=-10e^{-1}+10$
$=10-10e^{-1}=10\left( 1-\frac{1}{e}\right)=10\left( \frac{e-1}{e}\right)$