How can I quickly integrate 6e^-2t using simple techniques?

[pinkyjoshi65]

integration---very simple..need help fast!

how to integrate 6e^-2t

 

[Ben Niehoff]

Yes, it is very simple. What's confusing you about it, exactly?

 

[pinkyjoshi65]

dont know how to do it..lyke integal of it is 6*-0.5*e^-2t?

 

[Feldoh]

Looks right...

 

[pinkyjoshi65]

so now suppose i want to put in values for t as 0 and 6..will i get the answer as 2.99?

 

[Ben Niehoff]

No, not at all.

Edit: No, wait, maybe. I read it wrong. I assume you know how to use a calculator, though...I don't see what you're asking help with anymore.

 

[transgalactic]

(e^-2t)/-3

 

[Feldoh]

so now suppose i want to put in values for t as 0 and 6..will i get the answer as 2.99?

Yes you will get something like 2.99998

(e^-2t)/-3

Huh?

 

[transgalactic]

aaahhh sorryy its
-3*(e^-2t)

 

[fermio]

$$\int 6e^{-2x}dx=6\int e^{-2x}\frac{d(-2x)}{-2}=-3\int e^{-2x}d(-2x)=-3 e^{-2x}+C$$
where $$d(-2x)=-2dx$$
$$dx=\frac{d(-2x)}{-2}$$