# definite integrals

• Mar 23rd 2010, 06:44 PM
gearshifter
definite integrals
if anyone can help me with this, that would be great!
this is from ln3 to ln2
∫ 3/(e^(3t)) dt=???
• Mar 23rd 2010, 06:58 PM
dedust
Quote:

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 $\displaystyle \int e^{at} ~dt= \frac{1}{a}e^{at}$
• Mar 24th 2010, 11:41 AM
gearshifter
what do I do with the 3 on top?
• Mar 24th 2010, 11:57 AM
harish21
Quote:

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 $\displaystyle u = 3t$

then, $\displaystyle du = 3 dt$

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

so you have

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

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

substitute u = 3t, you get

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

calculate the value for the given upper and lower limits