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 $\int_{0}^{4}\,e^x\,dx$?
$\int_{0}^{4}\,e^x\,dx =$

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

 LEFT(2) RIGHT(2) TRAP(2) MID(2) SIMP(2) value error

(c)
Repeat part (b) with $n=4$ (instead of $n=2$).

 LEFT(4) RIGHT(4) TRAP(4) MID(4) SIMP(4) value error

(d)
For each rule in part (b), as $n$ goes from $n=2$ to $n=4$, does the error go down approximately as you would expect? Explain by calculating the ratios of the errors:
Error LEFT(2)/Error LEFT(4) =
Error RIGHT(2)/Error RIGHT(4) =
Error TRAP(2)/Error TRAP(4) =
Error MID(2)/Error MID(4) =
Error SIMP(2)/Error SIMP(4) =
(Be sure that you can explain in words why these do (or don't) make sense.)