$(1$ point$)$ Note: for this problem, because later answers depend on earlier ones, you must enter answers for all answer blanks for the problem to be correctly graded. If you would like to get feedback before you completed all computations, enter a $"1"$ for each answer you did not yet compute and then submit the problem. $($But note that this will, obviously, result in a problem submission.$)$

$($a$)$ What is the exact value of ${\displaystyle \underset{0}{\overset{4}{}}}{e}^{x}dx?$

${\displaystyle \underset{0}{\overset{4}{}}}{e}^{x}dx=$

$($b$)$

Find LEFT$(2),$ RIGHT$(2),$ TRAP$(2),$ MID$(2),$ and SIMP$(2)$; compute the error for each.

$\backslash$table$[[,$LEFT$(2),$RIGHT$(2),$TRAP$(2),$MID$(2),$SIMP$(2)],[$value$,16\mathrm{.}778,123\mathrm{.}975,70\mathrm{.}376,45\mathrm{.}608,44\mathrm{.}314],[$error$,,,(e^4)-(70\mathrm{.}376),(e^4)-(45\mathrm{.}608),(e^4)-(44\mathrm{.}314{)}^3$the table response previously made appears to be wrong on the errors for trap, mid, and simp$2,$ as wewell as value in table b for left right trap mid simp and error on b for right antrap and trap