(b) Let f: [0, 2] R be the constant function f(x) = -2 for all r E [0, 2] and let g : [0, 2] → R be g(r) = x. Prove that f is R-S integrable with respect to g on [0, 2] and compute the value of | fdg.
(b) Let f: [0, 2] R be the constant function f(x) = -2 for all r E [0, 2] and let g : [0, 2] → R be g(r) = x. Prove that f is R-S integrable with respect to g on [0, 2] and compute the value of | fdg.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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Transcribed Image Text:-4 -
4.l4 J=-1,207 and f,giJ n be defund by
fen=x and ç= .
defomel by
defurd
(x)=
why s R-s mtegralle an th raperk tage],
) Explain
Cayante: s
c2.5
f dg.
Ansures;
snce falax
it Cuutineum an J- EL,25]
mono dne
ß
on J-fl,21), Anden by Mee ExTt ence Theerew ne
Kutegrable
ant
lücrea
my
fructin f is R
onI =[,25}, mal is,
S Kütegrable wih weperktoy
2.5
fda
exsb
del
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2.
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![8. Choose and work either (a) or (b), NOT BOTH.
(a) Let g be defined on J = [0,3.5] by g(x) = |x| and let f: J R be defined
r3.5
r3.5
by f(x)
= cos(2Tr). Explain why do the integrals of
f dg and
f dx
0.
r3.5
exist and compute
f d(2g(z) +3x).
(b) Let f: [0, 2] R be the constant function f(x) = -2 for all r E [0, 2] and let
g : [0, 2] R be g(r) = r². Prove that f is R-S integrable with respect to g
%3D
c2
on 0, 2] and compute the value of
| fdg.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F593ae5b5-3a23-4d06-a4e7-3654e88936cf%2Fd2221e20-c1fd-4832-a8d7-7ef74d4ffb48%2Frkadm8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. Choose and work either (a) or (b), NOT BOTH.
(a) Let g be defined on J = [0,3.5] by g(x) = |x| and let f: J R be defined
r3.5
r3.5
by f(x)
= cos(2Tr). Explain why do the integrals of
f dg and
f dx
0.
r3.5
exist and compute
f d(2g(z) +3x).
(b) Let f: [0, 2] R be the constant function f(x) = -2 for all r E [0, 2] and let
g : [0, 2] R be g(r) = r². Prove that f is R-S integrable with respect to g
%3D
c2
on 0, 2] and compute the value of
| fdg.
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