3) Simplify expressions containing the Unit impulse: \text { a. } \quad\left(t^{3}+3\right) B(t) \text { b. }\left[\sin \left(t^{2}-\pi / 2\right)\right] \delta(t) \text { c. } \quad e^{-2 t} \delta(t) \text

{ d. } \frac{\left(\omega^{2}+1\right)}{\left(\omega^{2}+9\right)} \delta(\omega-1) \text { e. } \int_{-m}^{\infty} \delta(t) e^{-j \omega t} d t \text { f. } \int_{-\infty}^{\infty} \delta(t-2) \cos \left(\frac{\pi t}{4}\right) d t \text { g } \int_{-\infty}^{\infty} e^{-2(x-t)} \delta(2-t) d t