(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.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.7: Inverse Functions
Problem 2SE: Why do we restrict the domain of the function f(x)=x2 to find the function's inverse?
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Question
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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