Suppose I c [-1, 1] is an interval. Define the indicator function, XI : [-1, 1]→R, by 1, хEI x1(x) := { 0, x ¢ I Show that XI is Riemann integrable on [-1, 1] by using the ɛ- definition of Riemann integrability. Furthermore, ifa and b are the endpoints of I, then | x1(x) dx = |b – a|
Suppose I c [-1, 1] is an interval. Define the indicator function, XI : [-1, 1]→R, by 1, хEI x1(x) := { 0, x ¢ I Show that XI is Riemann integrable on [-1, 1] by using the ɛ- definition of Riemann integrability. Furthermore, ifa and b are the endpoints of I, then | x1(x) dx = |b – a|
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 IC[-1, 1] is an interval. Define the indicator function, XI : [-1, 1]→R, by
x1(7) := {
1, хEI
x ¢ I
0,
Show that XI is Riemann integrable on [-1, 1] by using the &-definition of Riemann integrability.
Furthermore, if a and b are the endpoints of I, then
| xr(x) dx = |b – a|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9444f09-d451-4777-a726-2c28d1bfa98b%2Ffd7e06d2-9c4d-4a1e-b3c4-8b2afa942714%2F6mpgg4z4_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose IC[-1, 1] is an interval. Define the indicator function, XI : [-1, 1]→R, by
x1(7) := {
1, хEI
x ¢ I
0,
Show that XI is Riemann integrable on [-1, 1] by using the &-definition of Riemann integrability.
Furthermore, if a and b are the endpoints of I, then
| xr(x) dx = |b – a|
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