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Lesson Worksheet: Numerical Integration: Riemann Sums Mathematics • Higher Education
In this worksheet, we will practice using right, left, and midpoint Riemann sums to numerically approximate definite integrals.
Q5:
Estimate using the midpoint rule with , giving your answer to four decimal places.
Q6:
Using the Midpoint Rule with , give an estimate of . Give your answer to four decimal places.
Q9:
Calculate the midpoint rule estimate of with subintervals. Is the result an overestimate or underestimate of the actual value?
- A16, an overestimate
- B16, an underestimate
- C48, an overestimate
- D28, an underestimate
- E28, an overestimate
Q10:
The table gives sampled values of an increasing function . Use the data to give a lower and upper bound for .
10 | 13 | 16 | 19 | 22 | 25 | |
1 | 4 | 8 | 10 |
- Alower bound: , upper bound: 1
- Blower bound: , upper bound: 20
- Clower bound: , upper bound: 3
- Dlower bound: , upper bound: 60
- Elower bound: , upper bound: 66