Consider f:0.2]R defined by: /(r)- if a 40 if r 0. Then 1. fs Riemann integrable over 0,2 and Lebsgue integrable over 2 2 fis Riemann ategrable over 0.2 but not Lebosgue integrable over 2 3. / is Lebesgue integrable.over (0.2) but not Riemann integrable over 2 1 is not Riemann integrable over 0,2 and not Lebesgue integrabikor

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider f: 0.2] R defined by: f(r)-
f1/
if r 40
if z 0.
Then
1. fs Riemann integrable over 0 2) and Lebngue integrable over 02
2. fis Riemann integrable over 0.2 but not Lebesgue integrable over
3. /is Lebesgue integrable.over (0.2) but not Riemann integrable over 2
4 is not Riemann integrable over 0.2 and not Lebesgue integrabile ovt
Transcribed Image Text:Consider f: 0.2] R defined by: f(r)- f1/ if r 40 if z 0. Then 1. fs Riemann integrable over 0 2) and Lebngue integrable over 02 2. fis Riemann integrable over 0.2 but not Lebesgue integrable over 3. /is Lebesgue integrable.over (0.2) but not Riemann integrable over 2 4 is not Riemann integrable over 0.2 and not Lebesgue integrabile ovt
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