Math Is Fun Forum

xingz

Member

Registered: 2008-03-23

Posts: 1

Integral problem

Can anyone help me out with this question?

Thanks a bunch!

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Integral problem

Hi xingz,

Let

Then

Also the limits change to -2+3=-1 and k+3

And as k goes to infinity the left fraction disappears, so we're left with 1.

Last edited by Identity (2008-03-23 16:58:21)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Integral problem

Was it necessary to use a substitution?

By inspection,

differentiates to

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Integral problem

Most substitutions are not necessary if you can do it in your head. With that said, it isnt necessary as you said but it simplifies the integral so its less troublesome for the people that are still learning.

Xingz, the integral you asked about is called an "improper integral" because your taking the integral over an infinite interval. As Identity mentioned, the way to handle such integral is to change the intervals such that:

In this case you have replaced infinity with k but since your taking the limit as k goes to infinity, its the same but it makes it possible for you to solve an otherwise unsolvable integral.