Boundaries Change With U-Sub? Huh?

[TranscendArcu]

So, I've been trying to figure out why the boundaries change in the example below. It seems like the boundaries change from [0,2] to [1,17] and I can't discover why this is. Ideas?

http://img841.imageshack.us/img841/3808/skjermbilde20111129kl52.png

 

[micromass]

You're just making a substitution. What is the theorem that says that you can calculate integrals by substitution?? What does it say about the bounds?

 

[TranscendArcu]

I don't know what theorem this is. What theorem is it?

 

[LCKurtz]

If u = 1+4t², what u values correspond to your t value limits?

 

[TranscendArcu]

Oh! I understand this now: 4t² + 1, where t=2,0 gives 17 and 1, respectively.

Okay. But, just out of curiosity, what theorem is this? I still don't know.