This discussion focuses on solving integrals of the form \(\int f(v) e^{iavx} dv\) and the treatment of the imaginary unit \(i\) as a constant. Participants confirm that \(i\) can be treated as a constant during integration, allowing the integral to be expressed as a combination of real and imaginary parts using Euler's formula: \(e^{i \phi} = \cos(\phi) + i \sin(\phi)\). The final expression derived is \(w(x) = \int_{-u_0}^{u_0} i2 \pi v e^{i2 \pi vx} dv = \frac{1}{\pi x^2} \left[ 2 \pi u_0 x \cos{(2 \pi u_0 x)} - \sin{(2 \pi u_0 x)} \right]\), confirming the correctness of the approach.
PREREQUISITESMathematicians, physics students, and engineers who are working with complex integrals and require a solid understanding of integrating functions involving complex exponentials.