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(c) Evaluate the Riemann integral tion Pn= 1, n+1 n+2 n n dx by using definition with the parti- 2n=1,2}, f'(x) ,, Hint: (1) Each (sub)interval is given by [n+i-1 n+i] n n 1 ≤ i ≤n. nEN.

(c) Evaluate the Riemann integral tion Pn= 1, n+1 n+2 n n dx by using definition with the parti- 2n=1,2}, f'(x) ,, Hint: (1) Each (sub)interval is given by [n+i-1 n+i] n n 1 ≤ i ≤n. nEN.

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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Let the function f: R → R be defined by 1 x2, f(x)= 0, x=0, x = 0.
Transcribed Image Text:Let the function f: R → R be defined by 1 x2, f(x)= 0, x=0, x = 0.
(c) 1 Evaluate the Riemann integral f(x) dx by using definition with the parti- tion P₁ = { 1, i=1 n+1 n+2 3 n 7 n n Hint: (1) Each (sub)interval is given by [n+i-1 n+i " .. #1], n 1-2-1, 2}, n 1≤ i ≤n. (2) Use the formulae Σ(n+i-1)³ = n²(15n² = 14n+3), (n+i)³ = = n²(15n² + 14n+3). nEN. i=1
Transcribed Image Text:(c) 1 Evaluate the Riemann integral f(x) dx by using definition with the parti- tion P₁ = { 1, i=1 n+1 n+2 3 n 7 n n Hint: (1) Each (sub)interval is given by [n+i-1 n+i " .. #1], n 1-2-1, 2}, n 1≤ i ≤n. (2) Use the formulae Σ(n+i-1)³ = n²(15n² = 14n+3), (n+i)³ = = n²(15n² + 14n+3). nEN. i=1
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