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