Question

The table gives the values of a function obtained from an experiment. Use them to estimate Ox) dx using three equal subintervals with right andpoints, left endpoints, and midpoints. 3 4 5 5 7 8 9 FO) -3.5 -2.1-0.70.2 0.8 1.4 1.8 (*) Estimate x) dx using three qual subintervals with right endpoints. R- ки If the function is known to increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? O than O greater than one cannot say (b) Estimate f x) dx using three equal subintervals with left andpoints of 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 less than O greater than one cannot say (c) Estimate ка x) dx using three equal subintervals with midpoints My 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 less than greater than one cannot say

Answer 1

To find 9 slal daar 3 Given that, 8 G 2 3 4 5 G 7 fla) 135 -2.) 0.7 0.2 0,8 64 1.8 Here a=3, 6=9, Exact valore = feasda_-20) (a) using three equal susintervals with right end points n=3 (b) Die 2 : Da=ban 9-333 = 0 =2 sufintervals are £3,5), 6,73 [ ] staz doa = Ox) [HC5)+4473+569)] R₂ =2[-0.7toast 1.8] = 3.8 Estimate value is greater than the Exact value of the integral left end points a n=3, Stayda = ®n) [f23)+F(57+ 347)) 2 (-3.5-0.7+0.8) L₂= -6.8 Estimate value is less than the Exact valore of the integral. three Equal subintervals with mild points n=3, D2=2, subintervals are £3.5],[5.7 ing] mid points of susintervals are 4, 5, 8 respectively ... Mz = Px) [f24)+feat Hes)) 2-2.J+0,27-4)=- Estimate value is greater Than Exact value of the integral ro