Math problem driving me bonkers

[Zieara]

Just got this problem on my Fourier Analysis homework and I've been spinning my wheels on it for a long while. Looks simple enough, but I can't seem to seal the deal on it ; ;

f has period p. prove that for all real numbers d,

the integral of f from d to d+p is equal to the integral of f from 0 to p.

I tried using the integral identity: f from a to b is equal to f from a to c plus f from c to b.
But can't seem to get it from that. Also tried flipping some of these to get some to cancel out and it's a no go.

Any hints/tips/tricks to prove this sucker would be appreciated, thanks!

[Eliseos]

I am really not good at proof problems, but can't you just use the definition of a periodic function to prove that? Since f(x) = f(x+p), integral(f(x)) should be = integral(f(x+p)). Then use F(d+p) - F(d) = F(p) - F(0) by the fundamental theorem of calculus.

[willriker]

Then use F(d+p) - F(d) = F(p) - F(0) by the fundamental theorem of calculus.

this is where you lost me.

[Eliseos]

F is just the antiderivitive of f in my notation, so just evaluating the integral from d to d+p and 0 to p.

[Zieara]

yeah, I tried approaching it with the fundamental thm of calc. Still wasn't able to get the result I needed. The hint in the text says specifically to use that identity that I had in the OP, what else I need to do is beyond me at this point.

[Eliseos]

That hint is how you would normally compute an integral in fourier series, when you have a point in the integral that isn't continuous. Say if you had a signal whose slope was x from 0 to 1 and (-x+1) from 1 to 2, so you'd just separate the integral into two parts but I'm sure you know that already. The only thing I can think of to try is to use the letters d and p instead of actual numbers. I can check my circuits textbook when I get home to see if they mention anything on it in the fourier analysis chapter.

EDIT: If you wouldn't mind, would you post the calculations you've done so far, and include the steps in it. I always make stupid mistakes when I calculate things, and don't see when I transpose minus signs or can't add properly until someone else points it out.

[Zieara]

Using the identity in the OP I can get:

Int(f(x),d,d+p)= Int(f(x),0,p)+Int(f(x),d,0)+Int(f(x),p,d+p)

I either need to do something else, or find a way to cancel out the two rightmost integrals on the right hand side.

[Eliseos]

Int(f(x), 0, p) = F(p)-F(0)
Int(f(x), d, 0) = F(0)-F(d)
Int(f(x), p, d+p) = F(d+p)-F(p)
Int(f(x), d, d+p) = F(d+p) - F(d)

F(d+p) - F(d) = F(p) -F(0) + F(0) -F (d) +F(d+p) - F(p)

F(p)'s cancel, F(0)'s cancel and the two sides equate. Again I'm using the F(x) notation as that being the definite integral at that point.

[Zieara]

I need to end up with

Int(f(x),d,d+p)=Int(f(x),0,p)

though.

[Eliseos]

How did you get to:

Int(f(x),d,d+p)= Int(f(x),0,p)+Int(f(x),d,0)+Int(f(x),p,d+p)

Did you switch limits of integration of Int(f(x), 0, d) and negate it, then move it to the other side?

EDIT: It doesn't seem right to me to make Int(f(x), d, d+p) to Int(f(x), 0, d) + Int(f(x), d, d+p). You can't guarantee that the period goes through zero, nor that it is a single complete period. You can split up Int(f(x), 0, p) to Int(f(x), 0, d) + Int (f(x), d, p).

[Zieara]

Int(f(x),d,d+p)=Int(f(x),d,0)+Int(f(x),0,d+p)=Int( f(x),d,0)+Int(f(x),0,p)+Int(f(x),p,d+p)

Is how I got there, no fancy tricks, just using that identity twice.

[Cadsuane]

Just got this problem on my Fourier Analysis homework and I've been spinning my wheels on it for a long while. Looks simple enough, but I can't seem to seal the deal on it ; ;

f has period p. prove that for all real numbers d,

the integral of f from d to d+p is equal to the integral of f from 0 to p.

I tried using the integral identity: f from a to b is equal to f from a to c plus f from c to b.
But can't seem to get it from that. Also tried flipping some of these to get some to cancel out and it's a no go.

Any hints/tips/tricks to prove this sucker would be appreciated, thanks!

Seems like you're going to need to use some fact about periodic functions to prove it. If you have a definition for a periodic function you're supposed to use, that would help.

Edit: here's one. Suppose f: D => R is a function and f(x+np)=f(x), for all x in D and p is some real number, n is an integer, then f is a periodic function. That should make this pretty easy.

[Trelution]

Can't offer any help, but the title made me nostalgia on this, so thanks for that!

http://www.youtube.com/watch?v=4znEmzIywxM

[Gunitsoldier]

Don't know shit bout math but I just have to do this:

http://www.promonews.tv/wordpress/wp...dizzie-460.jpg

[Richybear]

This is why you need to ditch school and come back to FFXI full-time Zark.