Suppose Ic[-1, 1] is an interval. Define the indicator function, XI : [-1, 1]→R, by { 1, x e I 0, x ¢ I X1(x):= (1) Show that XI is Riemann integrable on [-1, 1] by using the ɛ-definition of Riemann integrability. (2) Show if a and b are the endpoints of I, then X1(x) dx = |b – a| |3D
Suppose Ic[-1, 1] is an interval. Define the indicator function, XI : [-1, 1]→R, by { 1, x e I 0, x ¢ I X1(x):= (1) Show that XI is Riemann integrable on [-1, 1] by using the ɛ-definition of Riemann integrability. (2) Show if a and b are the endpoints of I, then X1(x) dx = |b – a| |3D
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
{
1, х€I
X1(x)
0,
x ¢ I
(1) Show that XI is Riemann integrable on [-1, 1] by using the ɛ - definition of Riemann
integrability.
(2) Show if a and b are the endpoints of I, then
X1(x) dx = |b – a|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9444f09-d451-4777-a726-2c28d1bfa98b%2Fff701370-c03c-49f4-a4bd-eec3b3334c87%2F32vh7yh_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
{
1, х€I
X1(x)
0,
x ¢ I
(1) Show that XI is Riemann integrable on [-1, 1] by using the ɛ - definition of Riemann
integrability.
(2) Show if a and b are the endpoints of I, then
X1(x) dx = |b – a|
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