Real Analysis 1- Using the 2nd photo solution as an example, solve similarly the problem 8B -4 -4.l4 J=-1,207 and f,giJ n be defund byfen=x and ç= .defomel bydefurd(x)=why s R-s mtegralle an th raperk tage],) ExplainCayante: sc2.5f dg.Ansures;snce falaxit Cuutineum an J- EL,25]mono dneßon J-fl,21), Anden by Mee ExTt ence Theerew neKutegrableantlücreamyfructin f is RonI =[,25}, mal is,S Kütegrable wih weperktoy2.5fdaexsbdel2.52.2.2.ot|tこく 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 definedr3.5r3.5by f(x)= cos(2Tr). Explain why do the integrals off dg andf dx0.r3.5exist and computef d(2g(z) +3x).(b) Let f: [0, 2] R be the constant function f(x) = -2 for all r E [0, 2] and letg : [0, 2] R be g(r) = r². Prove that f is R-S integrable with respect to g%3Dc2on 0, 2] and compute the value of| fdg.

Answered: Image /qna-images/answer/d2221e20-c1fd-4832-a8d7-7ef74d4ffb48.jpg

(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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 30EQ

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Question

Real Analysis 1- Using the 2nd photo solution as an example, solve similarly the problem 8B

-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
2.5
2.
2.
2.
ot|tこく

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.

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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