Question

Does this converge or diverge, if converge what is the value?

Answer 1

\[\int\limits_{0}^{\infty} 1/(x+2)(x+4)dx\]

Answer 2

from 0 to t, limt t->inf ... i guess it diverges

Answer 3

\[\lim_{n\to\infty}\int_{0}^{n}\frac{1}{2(x+2)}dx-\lim_{n\to\infty}\int_{0}^{n}\frac{1}{2(x+4)}dx\]

Answer 4

Yea eyust I know that much..just not sure how

Answer 5

actualy i beleive a comparison would be easier...

Answer 6

across how did u get that? I did not get that..

Answer 7

but either way is 100 percent valid

Answer 8

yea this is integration comparison test ... if the above integration diverges and the your series also diverges

Answer 9

okay so in my class we showed that \[\int\limits_{1}^{\infty} 1/x^p \] diverges if p is >1

Answer 10

we can compare your integral to the above intagral and show that it is for sure greater

Answer 11

if something is greater than i divergent integral, it also diverges

Answer 12

yeah i saw that one time eyust..just not sure for this

Answer 13

across will prolly explain it better

Answer 14

heehe thats a long answer =P

Answer 15

okay so here we have the integral \[\int\limits_{1}^{\infty} 1/(x^2+6x+8)\]

and we could say that that integral is greater than
\[\int\limits_{1}^{\infty} 1/x^2 \]

and since

\[\int\limits_{1}^{\infty} 1/x^2 \] diverges, your inegral must also diverge

Answer 16

BTW all intergrals are w/ respect to x

Answer 17

its actually 0 to infinity. does that change it?

Answer 18

nope

Answer 19

but if it is less than 0 it would!

Answer 20

damn this is confusing. Oh well

Answer 21

yea i had a lot of troube with these once you get the hang of them tho they are super easy

Answer 22

basically an integral that diverges means that its area goes off to infinity or - infinity

Answer 23

an integral that converges means that its area becomes so small so fast that it might as well be equal to something

Answer 24

so if you are bigger than something that is already infinity, your definitly also infinity

Answer 25

and if you are smaller than something that is a finite number then you are definately also a finite number

Answer 26

alright thanks