(c) Evaluate the Riemann integral tion Pn ={1," i=1 n+1 n+2 n' n 1 dx by using definition with the parti- 2n-1 Hint: (1) Each (sub)interval is given by [n+i-1,nti], n 1 ≤n. ¹sisn. (2) Use the formulae Σ(n+i-1)³ = n²(15m² - 14n+3), 2(n+i)³ = n²(15n² +14n+3). i=1 n nEN.

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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Question

1c

(a)
(b)
(c)
Explain the differentiability of f on R by using definition.
Let f' be the first derivative of f computed in Q1(a). Explain why is Riemann
integrable on [1,2].
1
Evaluate the Riemann integral f(x) dx by using definition with the parti-
tion
2n=1,2},
Pn
={₁,
=
n+1 n+2
n
9
n
n
Hint: (1) Each (sub)interval is given by
n+i-1 n+i
nti
"
2+1].
n
1 ≤ i ≤n.
n
(2) Use the formulae
1
Σ(n+i − 1)³ = ²n² (15n² − 14n+3), (n+i) ³ = n²(15n² +14n+3).
i=1
nEN.
i=1
Transcribed Image Text:(a) (b) (c) Explain the differentiability of f on R by using definition. Let f' be the first derivative of f computed in Q1(a). Explain why is Riemann integrable on [1,2]. 1 Evaluate the Riemann integral f(x) dx by using definition with the parti- tion 2n=1,2}, Pn ={₁, = n+1 n+2 n 9 n n Hint: (1) Each (sub)interval is given by n+i-1 n+i nti " 2+1]. n 1 ≤ i ≤n. n (2) Use the formulae 1 Σ(n+i − 1)³ = ²n² (15n² − 14n+3), (n+i) ³ = n²(15n² +14n+3). i=1 nEN. i=1
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