Hi! There was a first part to this question to find the fourier series repesentation, I can do that fine but then I cant seem to get around this integral. I am studying for exams tomorrow so I'm going through past papers and this question comes up a lot so if anyone could help it would be really helpful! Thanks

The Fourier transforms of the function f(x) are given by

∞ ∞

A(λ) = ∫ f(x) cosλx dx, B(λ) = ∫ f(x) sin λx dx

-∞ -∞

with the Fourier Integral representation of f(x) given by

∞

f(x) = 1/pi ∫ A(λ) cosλx dx + B(λ)sin λx dx

0

The non-periodic function f is defined by

f(x) =1, −1 < x < 1

0, otherwise.

Obtain a Fourier integral representation for f(x).