# Can somebody check my work on this Fourier Series problem?

## Homework Statement ## Homework Equations  ## The Attempt at a Solution

Since P=2L, L=1 ?

a_o = 1/2 [ ∫(from -1 to 0) -dx + ∫(from 0 to 1) dx ] = 1/2 [ (0-1) + (1-0) ] = 1/2(0) = 0

a_n = - ∫ (from -1 to 0) cosnπx dx + ∫ (from 0 to 1) cosnπx dx = 0

b_n = - ∫ (from -1 to 0) sinnπx dx + (from 0 to 1) sinnπx dx = 2/nπ - 2/nπ*(cosnπ) = 2nπ / (1-cosnπ) = { 4/nπ n is odd ; 0 is even

The problem is my teacher has this as his answer: Am i doing something incorrectly?

Last edited:

Related Calculus and Beyond Homework Help News on Phys.org
Dr. Courtney
Gold Member
Why not check by graphing the original function and the Fourier series?

Why not check by graphing the original function and the Fourier series?
I understand you can check through graphing, but I just wanted some verification that my math is correct?

Wait L is suppose to equal 2 correct? Not 1?

Ray Vickson
Homework Helper
Dearly Missed
Wait L is suppose to equal 2 correct? Not 1?
If you mean that one period of the function goes from ##-L## to ##+L## then yes, of course ##L = 2##. That was implied in the question.

• Aristotle
If you mean that one period of the function goes from ##-L## to ##+L## then yes, of course ##L = 2##. That was implied in the question.
I figured...
For my b_n I got 2/(n*pi) [1 - cos(n*pi / 2 ).

Is this correct?

vela
Staff Emeritus