The table gives the values of a function obtained from an experiment. Use them to estimate 9 f(x) dx 3 using three equal subintervals with right endpoints, left endpoints, and midpoints

Question

x	3	4	5	6	7	8	9
f(x)	−3.4	−2.2	−0.5	0.2	0.8	1.4	1.8

(a) Estimate 9	f(x) dx
3

 using three equal subintervals with right endpoints.

R₃ =

If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral?

(b) Estimate 9	f(x) dx
3

 using three equal subintervals with left endpoints.

L₃ =

If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral?



Answer 1

Using the online calculator for Simpson's 3/8 rule, the area under this curve is

-1.0125