Solution-Use residue calculus to evaluate the integral

Use residue calculus to evaluate the integral

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Reference no: EM131077437

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.

Reference no: EM131077437

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Use residue calculus to evaluate the integral

Reference no: EM131077437

Reference no: EM131077437

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