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Determine the Riemann integral partitions given by Pn = Qn = {o, 0, 1 4 1 2 4n' 4n 3+n " 6 + 2n 4n 4n So 2x - 4x² dx by using definition, with the 0 n - 1 1 4n 1 1}, n€ N₁ on 0≤x≤ 2 4n - 3 4n " 1}, n nen, on 1 4 ≤ x ≤ 1.

Determine the Riemann integral partitions given by Pn = Qn = {o, 0, 1 4 1 2 4n' 4n 3+n " 6 + 2n 4n 4n So 2x - 4x² dx by using definition, with the 0 n - 1 1 4n 1 1}, n€ N₁ on 0≤x≤ 2 4n - 3 4n " 1}, n nen, on 1 4 ≤ x ≤ 1.

Advanced Engineering Mathematics
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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Determine the Riemann integral partitions given by Pn = Qn = { n 0, 1 2 4n' 4n 1 3+n 4 4n 4n £200- i=1 " Hint: Use the following formulae: n 6 + 2n So 2x - 4x² dx by using definition, with the 0 n-1 1 4n i=1 2 2 ne N, on 0≤x≤ ³,1}, 4n - 3 4n 2n (3(i-1) + n) - (3(i − 1) + n)² 2n(3i+n)-(3i+n)² n Σ2n(i − 1) – (i − 1)² = _n(4n² – 3n − 1), i=1 n Σ2ni - 12 i=1 = 1 nen, on ≤ x ≤ 1. 4 1 1 = n(4n² + 3n − 1), == ——2n(4n² == 9n+3), +9n+3).
Transcribed Image Text:Determine the Riemann integral partitions given by Pn = Qn = { n 0, 1 2 4n' 4n 1 3+n 4 4n 4n £200- i=1 " Hint: Use the following formulae: n 6 + 2n So 2x - 4x² dx by using definition, with the 0 n-1 1 4n i=1 2 2 ne N, on 0≤x≤ ³,1}, 4n - 3 4n 2n (3(i-1) + n) - (3(i − 1) + n)² 2n(3i+n)-(3i+n)² n Σ2n(i − 1) – (i − 1)² = _n(4n² – 3n − 1), i=1 n Σ2ni - 12 i=1 = 1 nen, on ≤ x ≤ 1. 4 1 1 = n(4n² + 3n − 1), == ——2n(4n² == 9n+3), +9n+3).
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