5 Let f: (0, 1]-→ R be continuous and non-decreasing, and P, n EN, be the partition1xo = 0,In-1=In = 1.....Show that the upper and lower Darboux sums satisfyf(1) – S(0)U(Pn) – L(Pn) =and therefore the Riemann integral f(x) dr exists.

Let f be a continuous and non decreasing function. Let P define the n partitions. Upper Darboux will…

5 Let f: [0, 1] –→R be continuous and non-decreasing, and P, n EN, be the partition 1 x0 = 0, #1 = n-1 In-1= In = 1. .... Show that the upper and lower Darboux sums satisfy (1) – S(0) U(Pm) – L(P,) = and therefore the Riemann integral f(x) dr exists.

5 Let f: [0, 1] –→R be continuous and non-decreasing, and P, n EN, be the partition 1 x0 = 0, #1 = n-1 In-1= In = 1. .... Show that the upper and lower Darboux sums satisfy (1) – S(0) U(Pm) – L(P,) = and therefore the Riemann integral f(x) dr exists.

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

5 Let f: (0, 1]-→ R be continuous and non-decreasing, and P, n EN, be the partition
1
xo = 0,
In-1=
In = 1.
....
Show that the upper and lower Darboux sums satisfy
f(1) – S(0)
U(Pn) – L(Pn) =
and therefore the Riemann integral f(x) dr exists.

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