# Fourier series integration help required.

## Homework Statement

I have a periodic function which has a period 2, which is defined as

f(x) = ( 1.7(x + 1) , -1 ≤ x < 0 With f(x+2) = f(x) for all x
( 1.7(x - 1), 0 < x ≤ 1

I have to determine a0

## The Attempt at a Solution

I have started this as

a0 = 1/T ∫ top limit = T/2 Bottom limit = -T/2 f(x) dx
= 1/2 ∫ top limit = 0 Bottom limit = -1. 1.7(x+1) dx + ∫Top limit 1, Bottom limit 0 1.7(x-1) dx.

Is this right what I am doing so far, the 1.7(x+1) and 1.7(x-1) part is confusing me should I make it 1.7x+1 and 1.7x-1 ? And how would I integrate them?

## Answers and Replies

LCKurtz
Science Advisor
Homework Helper
Gold Member
Have you drawn a picture of that function? Is it even, odd, or neither? Does that matter when calculating a0?

I haven't drawn it yet I have an example from my lecturer which is similar up until that point, when I have to integrate using 1.7(x+1) on the example there is no mention of odd or even numbers. I couldn't tell you if it mattered or not.

LCKurtz
Science Advisor
Homework Helper
Gold Member
I haven't drawn it yet I have an example from my lecturer which is similar up until that point, when I have to integrate using 1.7(x+1) on the example there is no mention of odd or even numbers. I couldn't tell you if it mattered or not.

I wasn't talking about odd or even numbers. It was about odd or even functions. Have you studied half-range Fourier expansions yet? Do you know what odd or even functions are and what that has to do with the coefficients?

No, we covered fourier series over an hour we didn't really get into it much we got a couple of pages of notes and some examples nothing like that was mentioned.

LCKurtz
Science Advisor
Homework Helper
Gold Member

## Homework Statement

I have a periodic function which has a period 2, which is defined as

f(x) = ( 1.7(x + 1) , -1 ≤ x < 0 With f(x+2) = f(x) for all x
( 1.7(x - 1), 0 < x ≤ 1

I have to determine a0

## The Attempt at a Solution

I have started this as

a0 = 1/T ∫ top limit = T/2 Bottom limit = -T/2 f(x) dx
= 1/2 ∫ top limit = 0 Bottom limit = -1. 1.7(x+1) dx + ∫Top limit 1, Bottom limit 0 1.7(x-1) dx.

Is this right what I am doing so far, the 1.7(x+1) and 1.7(x-1) part is confusing me should I make it 1.7x+1 and 1.7x-1 ? And how would I integrate them?

No, we covered fourier series over an hour we didn't really get into it much we got a couple of pages of notes and some examples nothing like that was mentioned.

OK. Well I was going to suggest a shortcut but you haven't covered it yet. So to answer your original question, first you need to correct the colored expressions above. You aren't removing parentheses correctly. a(x-1) = ax - a. Once you fix that your integrals should work. You should come up with a0= 0.

Hi thanks for the help things are starting to make sense now so just so i'm clear my expressions should be 1.7x + 1.7 and 1.7x - 1.7