A computer takes 2 seconds to compute a particular definite integral accurate to 4 decimal places. Approximately how long does it take the computer to get 12 decimal places of accuracy using each of the LEFT, MID, and SIMP rules?

Question

Round your answers to one decimal place.

(a) LEFT ¡Ö years

(b) MID ¡Ö hours

(c) SIMP ¡Ö minutes

Answer 1

(a) LEFT
For left hand or right hand rule, every extra digit requires 10 times of work. 4 digit needs 2 second. From 4 to 12, it has 8 digits. 2 * 10^(8) seconds / 60 /60 /24 /365 = 6.3 years
(b) MID
For midpoint rule, every 2 digit requires 10 times of work.
2 * 10^(8/2) /60 /60 = 5.6 hours
(c) SIMP
Each 4 digits requires 10 times of work.
2 * 10^(8/4) /60 = 3.3 mins.