A graphing calculator is recommended. Use a graphing calculator Riemann Sum (found here) to find the following Riemann sums. f(x) 2x from a = 1 to b=2 (a) Calculate the Riemann sum for the function for the following values of n: 10, 100, and 1,000. Use left, right, and midpoint rectangles, making a table of the answers, rounded to three decimal places. n 10 100 1,000 Left Midpoint Right (b) Find the exact value of the area under the curve by evaluating an appropriate definite integral using the Fundamental Theorem. The values of the Riemann sums from part (a) should approach this number. (Round your answer to three decimal places.) square units
A graphing calculator is recommended. Use a graphing calculator Riemann Sum (found here) to find the following Riemann sums. f(x) 2x from a = 1 to b=2 (a) Calculate the Riemann sum for the function for the following values of n: 10, 100, and 1,000. Use left, right, and midpoint rectangles, making a table of the answers, rounded to three decimal places. n 10 100 1,000 Left Midpoint Right (b) Find the exact value of the area under the curve by evaluating an appropriate definite integral using the Fundamental Theorem. The values of the Riemann sums from part (a) should approach this number. (Round your answer to three decimal places.) square units
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Riemann Sums and Definite Integrals**
A graphing calculator is recommended.
Use a graphing calculator [Riemann Sum (found here)] to find the following Riemann sums.
\[ f(x) = 2^x \, \text{from} \, a = 1 \, \text{to} \, b = 2 \]
---
**(a) Calculate the Riemann sum for the function for the following values of \( n \): 10, 100, and 1,000. Use left, right, and midpoint rectangles, making a table of the answers, rounded to three decimal places.**
| \( n \) | Left | Midpoint | Right |
|-----------|------|----------|-------|
| 10 | | | |
| 100 | | | |
| 1,000 | | | |
---
**(b) Find the exact value of the area under the curve by evaluating an appropriate definite integral using the Fundamental Theorem. The values of the Riemann sums from part (a) should approach this number. (Round your answer to three decimal places.)**
\[ \_\_\_\_\_ \, \text{square units} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F62ee504c-8559-4d00-bc97-de19563b806a%2F5b54b075-5a15-41ab-bf92-0fde1c7bc9d4%2F75n5bxp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Riemann Sums and Definite Integrals**
A graphing calculator is recommended.
Use a graphing calculator [Riemann Sum (found here)] to find the following Riemann sums.
\[ f(x) = 2^x \, \text{from} \, a = 1 \, \text{to} \, b = 2 \]
---
**(a) Calculate the Riemann sum for the function for the following values of \( n \): 10, 100, and 1,000. Use left, right, and midpoint rectangles, making a table of the answers, rounded to three decimal places.**
| \( n \) | Left | Midpoint | Right |
|-----------|------|----------|-------|
| 10 | | | |
| 100 | | | |
| 1,000 | | | |
---
**(b) Find the exact value of the area under the curve by evaluating an appropriate definite integral using the Fundamental Theorem. The values of the Riemann sums from part (a) should approach this number. (Round your answer to three decimal places.)**
\[ \_\_\_\_\_ \, \text{square units} \]
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