Can someone please rewrite this proof? The question is below: Suppose f: [0, 1] → R and g: [0, 1] → Rare such that for all x E (0, 1), we have f(x) = g(x). Suppose f is Riemann integrable. f Prove that g is Riemann integrable and integral from 0 to 1 of f = integral from 0 to 1 g detsum,mn mbintenabM-1nd, 1} and consider the right RiemannninR₁ = = f(h)1=1== ONow,2{ 0, h = 1,...,n/partition [0,1] intaHence,Lince,f, no,and,-since, him. Premann integrable1Show da = lim Rn = 0bma= 0h in Riemann integrablef-h is also Riemann integrableSit-us=on [0, 1],StonS's - S'ufh0in Riemann integrable onS'o = 1/s0[0,1] and no ison [0,1][0, 1] and Let, hi [0, 1] → R defined by h(x) = fexs-g(x) *x.Then, hex) = { 0, KE (0,1]fco)-g(0), x = 0Hence or in discontinuous onfraint in [0,1].Hence, using Lebesgue's Integrability Criterion hiRiemann integrable on [0, 1].atmastone

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Suppose f: [0, 1] → R and g: [0, 1] → Rare such that for all x E (0, 1), we have f(x) = g(x). Suppose f is Riemann integrable. f Prove that g is Riemann integrable and integral from 0 to 1 of f = integral from 0 to 1 g

Suppose f: [0, 1] → R and g: [0, 1] → Rare such that for all x E (0, 1), we have f(x) = g(x). Suppose f is Riemann integrable. f Prove that g is Riemann integrable and integral from 0 to 1 of f = integral from 0 to 1 g

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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Can someone please rewrite this proof? The question is below:

det
sum,
m
n mbintenab
M-1
nd, 1} and consider the right Riemann
ni
n
R₁ = = f(h)
1=1
== O
Now,
2
{ 0, h = 1,...,
n/
partition [0,1] inta
Hence,
Lince,
f, no,
and,
-
since, him. Premann integrable
1
Show da = lim Rn = 0
b
ma
= 0
h in Riemann integrable
f-h is also Riemann integrable
Sit-us
=
on [0, 1],
St
on
S's - S'u
f
h
0
in Riemann integrable on
S'o = 1/s
0
[0,1] and no is
on [0,1]
[0, 1] and

Let, hi [0, 1] → R defined by h(x) = fexs-g(x) *x.
Then, hex) = { 0, KE (0,1]
fco)-g(0), x = 0
Hence or in discontinuous on
fraint in [0,1].
Hence, using Lebesgue's Integrability Criterion hi
Riemann integrable on [0, 1].
atmast
one

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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