2. A step function f on [a, b] is a function for which there are a finite number of disjoint intervals I,..., I, with [a, b] = I,U I, for which f is constant on each of the intervals. (a) Let I, be an interval with endpoints a; and b;. Suppose f (x)= c; on I;. Show that f is Riemann integrable on [a, b] and that %3| f = E c;(b; – a;). i=1
2. A step function f on [a, b] is a function for which there are a finite number of disjoint intervals I,..., I, with [a, b] = I,U I, for which f is constant on each of the intervals. (a) Let I, be an interval with endpoints a; and b;. Suppose f (x)= c; on I;. Show that f is Riemann integrable on [a, b] and that %3| f = E c;(b; – a;). i=1
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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A step function f on [a, b] is a function for which there are a finite number of disjoint
intervals Ib ... , I. with [a, b] = I 1 u · · ·ui. for which f is constant on each of the
intervals.
![S Ci(b; – a;).
2. A step function f on [a, b] is a function for which there are a finite number of disjoint
intervals I1,..., I, with [a, b] =I,U I, for which f is constant on each of the
intervals.
(a) Let I; be an interval with endpoints a; and b;. Suppose f(x)= c; on I;. Show that
f is Riemann integrable on [a, b] and that
f = E c;(b; – a;).
i=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F187d6ce3-f16e-4919-9795-1c801fb3fce4%2F99741a91-68ab-45ca-91dd-c18bf4701e76%2Fg15nxlp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:S Ci(b; – a;).
2. A step function f on [a, b] is a function for which there are a finite number of disjoint
intervals I1,..., I, with [a, b] =I,U I, for which f is constant on each of the
intervals.
(a) Let I; be an interval with endpoints a; and b;. Suppose f(x)= c; on I;. Show that
f is Riemann integrable on [a, b] and that
f = E c;(b; – a;).
i=1
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