Lesson Worksheet: Numerical Integration: Riemann Sums Mathematics • Higher Education

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In this worksheet, we will practice using right, left, and midpoint Riemann sums to numerically approximate definite integrals.

Q1:

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

	5	7	9	11	13	15	17
				0.4	1.8	2.5	3.1

Q2:

Using the midpoint rule with , round to four decimal places.

Q3:

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

	1	2	3	4	5	6	7
					0.9	2.1	3.1

Q4:

Estimate using the midpoint rule with , giving your answer to four decimal places.

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.

Q7:

Approximate the integral using a Riemann sum with right endpoints. Take the number of rectangles to be 8.

Q8:

The table gives the values of a function obtained from an experiment. Use them to estimate using three equal subintervals with right endpoints.

	3	7	11	15	19	23	27
				0.8	2.3	3.4	4.8

Q9:

Calculate the midpoint rule estimate of with subintervals. Is the result an overestimate or underestimate of the actual value?

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

This lesson includes 5 additional questions and 99 additional question variations for subscribers.

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