Riemann Sum Tables - Problem Set - Left-Hand and Right-Hand Riemann Sums

Oct 8, 2026

Riemann Sum Tables worksheet for Infinite Calculus problems. Students approximate definite integrals by constructing left-hand and right-hand Riemann sums using given x- and f(x)-value tables, and optionally use a provided graph to sketch the function and the resulting sums. The sheet includes four left-hand integral tasks over intervals from 0 to 10 or 14 or 19, followed by four corresponding right-hand tasks using similar tabulated function values.

LanguageEnglish

CategoryExam

FormatPDF

Pages2

Reading Time5 min

AccessFree to download

Left-hand Riemann sum problems

Problem 1: ∫_0^10 f(x) dx

Problem 2: ∫_0^10 f(x) dx

Problem 3: ∫_0^14 f(x) dx

Problem 4: ∫_0^19 f(x) dx

Right-hand Riemann sum problems

Problem 3: ∫_0^14 f(x) dx

Problem 4: ∫_0^19 f(x) dx

Kuta Software-Infinite Calculus Name Riemann Sum Tables Date Period For each problem, use a left-hand Riemann sum to approximate the integral based off of the values in the table. You may use the provided graph to sketch the function data and Riemann sums. 1) ∫010 f (x) dx | x | 0 | 2 | 5 | 7 | 10 | | --- | --- | --- | --- | --- | --- | | f (x) | 2 | 3 | 5 | 7 | 8 | 2) ∫010 f (x) dx | x | 0 | 4 | 6 | 7 | 10 | | --- | --- | --- | --- | --- | --- | | f (x) | 5 | 3 | 2 | 3 | 5 | For each problem, use a right-hand Riemann sum to approximate the integral based off of the values in the table. You may use the provided graph to sketch the function data and Riemann sums. 3) ∫014 f (x) dx | x | 0 | 3 | 5 | 9 | 13 | 14 | | --- | --- | --- | --- | --- | --- | --- | | f (x) | −1 | −2 | −1 | 0 | −1 | 0 | f(x) 1 0.5 −0.5 −1 −1.5 −2 −2.5 −3 2 4 6 8 10 12 14 x 4) ∫019 f (x) dx | x | 0 | 4 | 9 | 10 | 12 | 19 | | --- | --- | --- | --- | --- | --- | --- | | f (x) | −3 | −5 | −4 | −2 | −1 | 1 | f(x) 2 1 −1 −2 −3 −4 −5 −6 2 4 6 8 10 12 14 16 18 x Kuta Software-Infinite Calculus Name Riemann Sum Tables Date Period For each problem, use a left-hand Riemann sum to approximate the integral based off of the values in the table. You may use the provided graph to sketch the function data and Riemann sums. 1) ∫010 f (x) dx | x | 0 | 2 | 5 | 7 | 10 | | --- | --- | --- | --- | --- | --- | | f (x) | 2 | 3 | 5 | 7 | 8 | −1 −1 1 2 3 4 5 6 7 8 9 10 x 44 2) ∫010 f (x) dx | x | 0 | 4 | 6 | 7 | 10 | | --- | --- | --- | --- | --- | --- | | f (x) | 5 | 3 | 2 | 3 | 5 | 37 For each problem, use a right-hand Riemann sum to approximate the integral based off of the values in the table. You may use the provided graph to sketch the function data and Riemann sums. 3) ∫014 f (x) dx | x | 0 | 3 | 5 | 9 | 13 | 14 | | --- | --- | --- | --- | --- | --- | --- | | f (x) | −1 | −2 | −1 | 0 | −1 | 0 | −12 4) ∫019 f (x) dx | x | 0 | 4 | 9 | 10 | 12 | 19 | | --- | --- | --- | --- | --- | --- | --- | | f (x) | −3 | −5 | −4 | −2 | −1 | 1 | −37 Create your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)

FAQs

How do you approximate the integrals in this worksheet?

Use the left-hand or right-hand Riemann sum rule with the provided table values for x and f(x) to approximate each definite integral.

What role do the tables of x and f(x) play?

They provide the sample points and function heights needed to form each rectangle sum for the Riemann approximation.

Can you use the graph when solving these problems?

Yes. The worksheet suggests using the provided graph to sketch the function data and the Riemann sums to help visualize the approximation.

Oct 8, 2026

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