Worksheet: Left Endpoint Riemann Sum

In this worksheet, we will practice finding an approximated value of the area under a curve using left endpoint approximation.

Q1:

The table shows the values of a function obtained from an experiment. Estimate using three equal subintervals with left endpoints.

 𝑥 𝑓 ( 𝑥 ) 5 7 9 11 13 15 17 − 3 − 1 . 7 − 0 . 6 0.4 1.8 2.5 3.1

Q2:

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

Q3:

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

Q4:

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

Q5:

Given that and that , evaluate, to the nearest six decimal places, the Riemann sum for with six subintervals, taking the sample points to be left endpoints.

Q6:

The table shows the values of a function obtained from an experiment. Estimate using three equal subintervals with left endpoints.

 𝑥 𝑓 ( 𝑥 ) 2 6 10 14 18 22 26 − 3 . 8 − 2 . 8 − 1 . 6 − 0 . 7 − 0 . 2 0.6 1.7

Q7:

The table shows the values of a function obtained from an experiment. Estimate using three equal subintervals with left endpoints.

 𝑥 𝑓 ( 𝑥 ) 3 7 11 15 19 23 27 − 3 . 3 − 2 . 4 − 1 . 7 − 0 . 4 0.8 1.7 2.2

Q8:

The table shows the values of a function obtained from an experiment. Estimate using three equal subintervals with left endpoints.

 𝑥 𝑓 ( 𝑥 ) 4 5 6 7 8 9 10 − 2 . 9 − 2 − 0 . 9 0.1 1.5 2.4 3.1