$(15$ points$)$ By direct integration, find the Laplace transform F$($s$)$ and the region of convergence of F$($s$)$ forthe following signals where a and b are positive real numbers:$($a$)(2$ points$)($t$)($b$)(2$ points$)$ u$($t$)($c$)(3$ points$)$ eatu$($t$)($d$)(4$ points$)$ cos$($bt$)$ u$($t$)($e$)(4$ points$)$ sin$($bt$)$ u$($t$)2.(5$ points$)$ Compare the Fourier and Laplace transforms of the signalsf$($t$)=($t$)$g$($t$)=$ u$($t$).$ExplainF$()=$ F$($s$)|$s$=,$whileG$()6=$ G$($s$)|$s$=.$