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 ā«āā“ eĖ£ dx?
ā«āā“ eĖ£ dx = e^4-1
(b)
Find LEFT(2), RIGHT(2), TRAP(2), MID(2), and SIMP(2); compute the error for each.
LEFT(2) value 16.778, error [(e^(4))-(16.778)]
RIGHT(2) value 123.974, error [(e^(4)-123.974)]
TRAP(2) value 70.376, error -16.778
MID(2) value 45.607, error 7.99
SIMP(2) value 56.769, error -3.171
(c)
Repeat part (b) with n = 4 (instead of n = 2).
LEFT(4) value 31.193, error [e^(4)-31.193]
RIGHT(4) value 84.791, error [e^(4)-84.791]
TRAP(4) value 57.99, error -4.394
MID(4) value 51.428, error 2.17
SIMP(4) value 53.864, error -0.266
(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) = 1.643
Error RIGHT(2)/Error RIGHT(4) = 2.256
Error TRAP(2)/Error TRAP(4) = 3.818
Error MID(2)/Error MID(4) = 3.682
Error SIMP(2)/Error SIMP(4) = 11.921
(Be sure that you can explain in words why these do (or don't) make sense.)