(a) (10 points) Let X(jw) denote the Fourier transform of the signal x(t) sketched below:(4) Evaluate the following quantities without explicitly finding X(jw): \text { i. } \int_{0}^{\infty} X(j \omega)

d \omega \text { ii. }\left.X(j \omega)\right|_{\omega=0} \text { iii. } / X(j \omega) \text { iv. } \int_{-\infty}^{\infty} e^{-j \omega} X(j \omega) d \omega \text { v. Plot the inverse Fourier transform of } \mathcal{R} e\left\{e^{-3 j \omega} X(j \omega)\right\} (b) (5 points) By first expressing the triangular signal x(t) shown below as the convolutionof a rectangular pulse with itself, determine the Fourier transform of x(t).