Riemann Sums Worksheet

Explore the concept of Riemann sums, approximating definite integrals using rectangles, and understanding the limit definition of the definite integral.

Grade 12 Math CalculusRiemann Sum

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2 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HS.C.A.1CCSS.MATH.CONTENT.HS.C.A.2

Topics

CalculusRiemann SumsDefinite IntegralApproximation

7 sections · Free to use · Printable

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Riemann Sums Worksheet

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Explain in your own words the main purpose of a Riemann sum. Why do we use it in calculus?

2. For a strictly increasing function on an interval [a, b], which of the following statements is true regarding a left Riemann sum (LRS) and a right Riemann sum (RRS) with n subintervals?

LRS < RRS

RRS < LRS

LRS = RRS

Cannot be determined

3. The width of each subinterval in a Riemann sum is denoted by Δx, which is calculated as .

4. As the number of subintervals (n) approaches infinity, the Riemann sum approaches the exact value of the .

5. Approximate the area under the curve f(x) = x² + 1 from x = 0 to x = 4 using a Left Riemann Sum with 4 equal subintervals.

6. A Midpoint Riemann Sum generally provides a more accurate approximation of the definite integral than a Left or Right Riemann Sum for the same number of subintervals.

True

False