equivalent définitión of the lehnité intégral :R-R between a and b, given x = a+ k() for 0sksn: Lf.a, b) =D f(x)dx = lim 1,(f.a, b) iv) We call a function f: R R monotone increasing if x> y implies f(x) > f(y). Show that, if f is monotone increasing, then, for any a,b e R,a < b, and neN I,f,a,b) < J.f,a, b) v) Without formally proving it, explain why: lim J,f,a,b) = S(x)dx lim I,f,a, b)
equivalent définitión of the lehnité intégral :R-R between a and b, given x = a+ k() for 0sksn: Lf.a, b) =D f(x)dx = lim 1,(f.a, b) iv) We call a function f: R R monotone increasing if x> y implies f(x) > f(y). Show that, if f is monotone increasing, then, for any a,b e R,a < b, and neN I,f,a,b) < J.f,a, b) v) Without formally proving it, explain why: lim J,f,a,b) = S(x)dx lim I,f,a, b)
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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Transcribed Image Text:c) Below is an alternative but equivalent definition of the definite integral of f: R R
between a and b, given xg = a + k() for 0sksn:
n-1
k=0
|f(x)dx = lim I,(f ,a, b)
iv) We call a function f: R-R monotone increasing if x> y implies f(x) > f(y).
Show that, if f is monotone increasing, then, for any a,be R, a < b, and neN
I„f,a, b) < J„(f,a, b)
v) Without formally proving it, explain why:
JS.a,b) = F
lim
f(x)dx = lim I,f,a, b)
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