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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 52E
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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.
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