2.4-4 Evaluate the following integrals:
(a) $\int_{-\infty}^{\infty} g(-3\tau + a)\delta(t - \tau) d\tau$
(b) $\int_{-\infty}^{\infty} \delta(\tau)g(t - \tau) d\tau$
(c) $\int_{-\infty}^{\infty} \delta(t + 2)e^{-j\omega t} dt$
(d) $\int_{-\infty}^{1} \delta(t - 2)\sin \pi t dt$
(e) $\int_{-2}^{\infty} \delta(2t + 3)e^{-4t} dt$
(f) $\int_{-2}^{2} (t^3 + 4)\delta(1 - t) dt$
(g) $\int_{-\infty}^{\infty} g(2 - t)\delta(3 - 0.5t) dt$
(h) $\int_{-\infty}^{\infty} \cos \frac{\pi}{2}(x - 5)\delta(3x - 1) dx$
Hint: $\delta(x)$ is located at $x = 0$. For example, $\delta(1 - t)$ is located at $1 - t = 0$, that is, at $t = 1$, and
so on.
