Consider the following definite integral. 10 0 (10x-x²) dx a. Write the midpoint Riemann sum in sigma notation for an arbitrary value of n. b. Evaluate the sum using a calculator with n = 20, 50, and 100. Use these values to estimate the value of the integral. a. Choose the correct Riemann sum below. A. n k=1 O c. Σ (k)(n-1) k=1 n (2k-1)(2n + 1-2k) k=1 250 n³ 250 OE. (k-1)(n+1-k) 3 250 b. Evaluate the sum using a calculator, with n = 20. The sum with n = 20 is 166.875 (Do not round until the final answer. Then round to four decimal places as needed.) Evaluate the sum using a calculator, with n = 50. The sum with n = 50 is. (Do not round until the final answer. Then round to four decimal places as needed.) OB. (2k-1)(2n +1 -2k) OD. OF. k=1 n k=1 (k)(n-1) 1000 n³ n Σ (k-1){(n+1−k) k=1 1000 1000 3 nº
Consider the following definite integral. 10 0 (10x-x²) dx a. Write the midpoint Riemann sum in sigma notation for an arbitrary value of n. b. Evaluate the sum using a calculator with n = 20, 50, and 100. Use these values to estimate the value of the integral. a. Choose the correct Riemann sum below. A. n k=1 O c. Σ (k)(n-1) k=1 n (2k-1)(2n + 1-2k) k=1 250 n³ 250 OE. (k-1)(n+1-k) 3 250 b. Evaluate the sum using a calculator, with n = 20. The sum with n = 20 is 166.875 (Do not round until the final answer. Then round to four decimal places as needed.) Evaluate the sum using a calculator, with n = 50. The sum with n = 50 is. (Do not round until the final answer. Then round to four decimal places as needed.) OB. (2k-1)(2n +1 -2k) OD. OF. k=1 n k=1 (k)(n-1) 1000 n³ n Σ (k-1){(n+1−k) k=1 1000 1000 3 nº
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the following definite integral.
10
0
(10x-
(10x-x²) dx
a. Write the midpoint Riemann sum in sigma notation for an arbitrary value of n.
b. Evaluate the sum using a calculator with n = 20, 50, and 100. Use these values to estimate the value of the integral.
a. Choose the correct Riemann sum below.
A.
n
k=1
Oc. Σ (k)(n-1)
k=1
n
(2k-1)(2n + 1-2k)
k=1
250
n³
250
n3
250
OE. (k-1)(n+1-k) 3
b. Evaluate the sum using a calculator, with n = 20.
The sum with n = 20 is 166.875
(Do not round until the final answer. Then round to four decimal places as needed.)
Evaluate the sum using a calculator, with n = 50.
The sum with n = 50 is.
(Do not round until the final answer. Then round to four decimal places as needed.)
OB. (2k-1)(2n+1-2k)
OD.
OF.
k=1
n
k=1
n
k=1
(k)(n-1)
1000
n³
(k-1)(n+1-k)
1000
1000
3
nº
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