Suppose f: [a, b] → R is Riemann integrable, that is, f = R([a, b]). Prove that 72 b fº* f(x) dx = lim ² Σƒ(a + j(b-a)) 11-0 a j=1 n
Suppose f: [a, b] → R is Riemann integrable, that is, f = R([a, b]). Prove that 72 b fº* f(x) dx = lim ² Σƒ(a + j(b-a)) 11-0 a j=1 n
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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![Suppose f [a, b] → R is Riemann integrable, that is, f = R([a, b]). Prove that
:
b
<- a
fo
f(x) dx = lim ² [ƒ(a + j(b= a))
11-0
n
n
a
j=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6429f7f6-5778-4799-8eb3-c38ae2520bd4%2Fba068385-8024-4892-8fb7-d44d1e67138e%2F7pxhfqj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose f [a, b] → R is Riemann integrable, that is, f = R([a, b]). Prove that
:
b
<- a
fo
f(x) dx = lim ² [ƒ(a + j(b= a))
11-0
n
n
a
j=1
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