In this assignment we look at the Fourier transformation detined by -idx f (x) - Serxle dx - sinx for function f(x) for which the integral converges a real). Afterwards we let for OLX LT Sinx f(x)= for TL xco for 181 > for x real. al show that the Fourier trans formed (A) of the above function f(x) is given by ( 1+cos XT VZT 1- x2 ) an Is (*) equal function ? Find the value in x=0 that b) Calculate the integral is lo). so itx + cos att 1-1 e da for arbitrary real. c) Calculate the integral |_tCos . di 1- x2 for example by using Planchere's theorem. 2 ( In this assignment we look at the Fourier transformation detined by -idx f (x) - Serxle dx - sinx for function f(x) for which the integral converges a real). Afterwards we let for OLX LT Sinx f(x)= for TL xco for 181 > for x real. al show that the Fourier trans formed (A) of the above function f(x) is given by ( 1+cos XT VZT 1- x2 ) an Is (*) equal function ? Find the value in x=0 that b) Calculate the integral is lo). so itx + cos att 1-1 e da for arbitrary real. c) Calculate the integral |_tCos . di 1- x2 for example by using Planchere's theorem. 2 (