$($a$)$ Find the function giving the number of mining industry jobs in year x $.($b$)$ Find the projected number of mining industry jobs in the year $2020.($a$)$ Set up the appropriate integral that can be used to find the number of mining industry jobs. $\backslash [\backslash$int$(\backslash$square$)$ d x $\backslash ]$ Let $\backslash (\backslash$mathrm$\{$m$\}(\backslash$mathrm$\{$x$\})\backslash )$ be the function that represents the number of mining industry jobs $($in thousands$)$ x years after $2000.$ Find $\backslash (\backslash$mathrm$\{$m$\}(\backslash$mathrm$\{$x$\})\backslash ).\backslash [\backslash$mathrm$\{$m$\}(\backslash$mathrm$\{$x$\})=\backslash$square $\backslash ]($Type an exact answer. Use parentheses to clearly denote the argument of each function.$)($b$)$ There will be thousand mining industry jobs in $2020.($Round to the nearest whole number as needed.$)$