Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 4 / a

Use the Fourier transform convention $\tilde{a}(\omega )={\int }_{-\infty }^{\infty }a(t)e^{-i\omega t}dt$, with inverse factor $1/(2\pi )$. Direct integration over the pulse givesThe apparent singularity at zero is removable. Changing the values of the pulse at its two endpoints does not affect the transform.