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Complete the following steps for the given function f and interval. a. For the given value of n, use sigma notation to write the left, right, and midpoint Riemann sums. Then evaluate each sum using a calculator. b. Based on the approximations found in part (a), estimate the area of the region bounded by the graph of f on the interval. f(x) = sin 2x for 0, ;n=40 a. Write the left Riemann sum. 40 k=1 (Type an exact answer, using n as needed.) The approximation of the left Riemann sum is. (Do not round until the final answer. Then round to three decimal places as needed.) Write the right Riemann sum. 40 Σ k=1 (Type an exact answer, using a as needed.) The approximation of the right Riemann sum is (Do not round until the final answer. Then round to three decimal places as needed.) Write the midpoint Riemann sum. 40 ΣΟ k=1 (Type an exact answer, using r as needed.) The approximation of the midpoint Riemann Sum is (Do not round until the final answer. Then round to three decimal places as needed.) b. The estimated area of the region, based on part (a), is approximately (Simplify your answer. Use the answers from part (a) to find this answer. Round to three decimal places as needed.) Mồ

Complete the following steps for the given function f and interval. a. For the given value of n, use sigma notation to write the left, right, and midpoint Riemann sums. Then evaluate each sum using a calculator. b. Based on the approximations found in part (a), estimate the area of the region bounded by the graph of f on the interval. f(x) = sin 2x for 0, ;n=40 a. Write the left Riemann sum. 40 k=1 (Type an exact answer, using n as needed.) The approximation of the left Riemann sum is. (Do not round until the final answer. Then round to three decimal places as needed.) Write the right Riemann sum. 40 Σ k=1 (Type an exact answer, using a as needed.) The approximation of the right Riemann sum is (Do not round until the final answer. Then round to three decimal places as needed.) Write the midpoint Riemann sum. 40 ΣΟ k=1 (Type an exact answer, using r as needed.) The approximation of the midpoint Riemann Sum is (Do not round until the final answer. Then round to three decimal places as needed.) b. The estimated area of the region, based on part (a), is approximately (Simplify your answer. Use the answers from part (a) to find this answer. Round to three decimal places as needed.) Mồ

Calculus: Early Transcendentals
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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Complete the following steps for the given function f and interval. a. For the given value of n, use sigma notation to write the left, right, and midpoint Riemann sums. Then evaluate each sum using a calculator. b. Based on the approximations found in part (a), estimate the area of the region bounded by the graph of f on the interval. f(x) = sin 2x for 0, ;n=40 a. Write the left Riemann sum. 40 Σ k= 1 (Type an exact answer, using n as needed.) The approximation of the left Riemann sum is| . (Do not round until the final answer. Then round to three decimal places as needed.) Write the right Riemann sum. 40 k= 1 (Type an exact answer, usingn as needed.) The approximation of the right Riemann sum is- (Do not round until the final answer. Then round to three decimal places as needed.) Write the midpoint Riemann sum. 40 Σ k= 1 (Type an exact answer, using n as needed.) The approximation of the midpoint Riemann Sum is. (Do not round until the final answer. Then round to three decimal places as needed.) b. The estimated area of the region, based on part (a), is approximately. (Simplify your answer. Use the answers from part (a) to find this answer. Round to three decimal places as needed.) Enter vOur answwer in each of the answer boxes
Transcribed Image Text:Complete the following steps for the given function f and interval. a. For the given value of n, use sigma notation to write the left, right, and midpoint Riemann sums. Then evaluate each sum using a calculator. b. Based on the approximations found in part (a), estimate the area of the region bounded by the graph of f on the interval. f(x) = sin 2x for 0, ;n=40 a. Write the left Riemann sum. 40 Σ k= 1 (Type an exact answer, using n as needed.) The approximation of the left Riemann sum is| . (Do not round until the final answer. Then round to three decimal places as needed.) Write the right Riemann sum. 40 k= 1 (Type an exact answer, usingn as needed.) The approximation of the right Riemann sum is- (Do not round until the final answer. Then round to three decimal places as needed.) Write the midpoint Riemann sum. 40 Σ k= 1 (Type an exact answer, using n as needed.) The approximation of the midpoint Riemann Sum is. (Do not round until the final answer. Then round to three decimal places as needed.) b. The estimated area of the region, based on part (a), is approximately. (Simplify your answer. Use the answers from part (a) to find this answer. Round to three decimal places as needed.) Enter vOur answwer in each of the answer boxes
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