Math Is Fun Forum

Tredici

Member

Registered: 2005-12-12

Posts: 28

Probably simple C4 Integration

I'll probably be here a lot recently, considering the core and mechanics revision, so I hope I don't end up flooding this place with questions left, right and centre. If you happen to know of C4 papers worked through, i.e. not just the answers, it would be of great help. Here's the question:

It's probably very simple, as I've said, and I'd like to add, I'd really appreciate it if it were worked through thoroughly, as I'm not looking for answers; I'm looking to understand how you've answered it, which can then be applied to similar questions. Thanks chaps, you've always been of great help to me.

Tredici

Member

Registered: 2005-12-12

Posts: 28

Re: Probably simple C4 Integration

I have the answer, if it's of help:

Although it's smack bang in front of me, I still can't understand it, so could anyone work it through for me? Cheers, Tredici.

Last edited by Tredici (2006-05-16 08:52:16)

Tredici

Member

Registered: 2005-12-12

Posts: 28

Re: Probably simple C4 Integration

I really hate to bump threads guys, and I'm sorry, but I'd really appreciate a walkthrough of this question within about 5 hours; when C4 classes start.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Probably simple C4 Integration

It's basically just a simple subsitution.  Do you understand other substitutions?  Like for example:

You would let x = 1/2 u and so dx = 1/2du.  So the integral becomes:

We do the same thing for your equation, expect you use x = tan u.  To get I, you have:

Because:

If you are still unsure, can you name specifically what part you don't get?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

liuv

Member

Registered: 2006-05-14

Posts: 29

Re: Probably simple C4 Integration

let  x=tan(p) p∈[0,Pi/4]
     dx=sec^2(p)*dp
     1+tan^2(p)=sec^2(p)
     dx/(1+tan^2(p))^2=1/(sec^2(p))=cos^2(p)
     cos(2p)=2cos^2(p)-1

Last edited by liuv (2006-05-16 20:00:30)

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Tredici

Member

Registered: 2005-12-12

Posts: 28

Re: Probably simple C4 Integration

Yeah, I see where I've went wrong. I began to plug in limits when it was all relative to dx, forgot to do the whole dx/dθ=sec²θ and rearrange that to replace dx. Thanks a bunch guys, again. You've been a fantastic help.