# Math Help - definite integrals

1. ## definite integrals

if anyone can help me with this, that would be great!
this is from ln3 to ln2
∫ 3/(e^(3t)) dt=???

2. Originally Posted by gearshifter
if anyone can help me with this, that would be great!
this is from ln3 to ln2
∫ 3/(e^(3t)) dt=???
use the formula $\int e^{at} ~dt= \frac{1}{a}e^{at}$

3. what do I do with the 3 on top?

4. Originally Posted by gearshifter
if anyone can help me with this, that would be great!
this is from ln3 to ln2
∫ 3/(e^(3t)) dt=???
If you are not getting what the above post says:

let $u = 3t$

then, $du = 3 dt$

so, $dt= \frac{du}{3}$

so you have

$\int_{ln3}^{ln2} {3 e^{-u}}\frac{du}{3}$

= $[-e^{-u}]_{ln3}^{ln2}$

substitute u = 3t, you get

$[-e^{-3t}]_{ln3}^{ln2}$

calculate the value for the given upper and lower limits