Let the function ƒ : [0, 1] →R be defined by { if x = ! (n = 1, 2, 3, · · · ) f(x) = n 1– x2 otherwise (a) Show that f is a measurable function. (b) Evaluate | f dx.
Let the function ƒ : [0, 1] →R be defined by { if x = ! (n = 1, 2, 3, · · · ) f(x) = n 1– x2 otherwise (a) Show that f is a measurable function. (b) Evaluate | f dx.
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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Transcribed Image Text:Let the function f : 0, 1| –→ R be defined by
{
(n = 1, 2, 3, -..)
it x =
f(x) =
1 – x²
.2
otherwise
(a) Show that f is a measurable function.
(b) Evaluate
| f dx.
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