Question

Can anyone help me with this integral? im not sure what i am suppose to do with it

Answer 1

\[\int\limits\limits_{0}^{infinity} e^(-\theta*x)(1/3)e^(-x/3)dx\]

Answer 2

where theta >0

Answer 3

Tried solving it ?

Answer 4

ya i have the problem i come into is that i get different values for differnt thetas

Answer 5

what makes sense i think so im not sure what im suppose to do with it

Answer 6

\[\int\limits\limits\limits_{0}^{infty } e^{-\theta*x}(1/3)e^{-x/3}dx \]

This is the correct ques?

Answer 7

yes that is correct

Answer 8

so i did a simmilar question which was the same thing but without the e^(-theta*x) part and i got 3 with i know is right

Answer 9

int\limits\limits_{0}^{infinity} e^(-\theta*x)(1/3)e^(-x/3)dx theta >0 (apparantly)

Answer 10

but there are only limits for x so how should i solve it?

Answer 11

well it would be e^(-x^2/3) i think

Answer 12

ya sorry that should be in there too

Answer 13

so make x = ((-x*theta)/3)

Answer 14

then im guessing after computing there will be a answer that is dependent on theta?

Answer 15

well then its e^x with does not converge

Answer 16

For infinite limits,you take the integral from [0, R] and then take the limit as R->∞

Answer 17

sorry, for improper integrals* my mistake.

Answer 18

Also note: \[\int\limits_{a}^{∞} \frac{ 1 }{ x^R }dx\]
p>1 (convergent)
p<1 (divergent)

Answer 19

so how does that help me?

Answer 20

idk. i'm just throwing random stuff out there I guess.

Answer 21

lol