Math 121a homework 10 use residue calculus to evaluate the

Question

Math 121A: Homework 10-

1. Consider the function

f(x) = 1/1 + x⁴.

Calculate its Fourier transform f^˜(α) using residue calculus, for the range α ≥ 0. For α < 0, find the solution using symmetry.

2. Use residue calculus to evaluate the integral

I = _-∞∫^∞(1 - cos x/x²)dx.