Calc 2 help needed

[Trezza]

I am doing something new in calc 2 were we show that improper integrals converge by the comparison therum. I understand that and all but how can i figure out what integrals are similar.

For example the integral 1/ (sqrt x + x^4) on [0 to inf] what is a similar problem to compare this one to or more generally how do you pick integrals that are similar to your problem?

 

[Trezza]

anyone?

 

[shady123]

 

[DanJ]

Dude just change majors. It only gets worse.

 

[phreakah]

Originally posted by: DanJ
Dude just change majors. It only gets worse.

^^^ ditto

 

[Trezza]

all i need to do i get c's in this and linear algebra and i am done with math for my major.

 

[jaydee]

You have to pick a known integral that converges and prove that the integral you're testing is smaller than that.

Or, pick a known integral that diverges and prove the one you're testing is bigger than that.

That's all the comparison test is.

 

[jaydee]

By far, the most useful example:

Int(1/x^p):

Convergent if p >1

Divergent if p </= 1

Edit: And if it's convergent don't forget to figure out what it's converging to.

 

[Trezza]

Originally posted by: jaydee
By far, the most useful example:

Int(1/x^p):

Convergent if p >1

Divergent if p </= 1

i didn't think of 1/x^p got stuck on the sqrt wasn't thinking i could change it to (x+x^4)^1/2

you sir are a genius