EXERCISE 3.15 Let a > 0. Use the fact that sinc(x), sinc²(x) have the Fourier
transforms Π(s), A(s) together with a suitably chosen synthesis equation, Parseval's relation, ... to show that:
(a)
$$ \int_{-\infty}^{\infty} \left( \frac{\sin ax}{x} \right) dx = \pi; $$
(b)
$$ \int_{-\infty}^{\infty} \left( \frac{\sin ax}{x} \right)^2 dx = a\pi; $$
(c)
$$ \int_{-\infty}^{\infty} \left( \frac{\sin ax}{x} \right)^3 dx = \frac{3a^2 \pi}{4}; $$
(d)
$$ \int_{-\infty}^{\infty} \left( \frac{\sin ax}{x} \right)^4 dx = \frac{2a^3 \pi}{3}. $$