Let f be an integrable function on [0, 1] . a) Which of the following inequalities is true: i) ſexp (f (x)) dx > exp ( Sf (x) dx ); 1 ii) ſexp (f (x)) dx < exp ( Sf (x) dx Explain your answer. b) when do we have equality in a)? Explain your answer.
Let f be an integrable function on [0, 1] . a) Which of the following inequalities is true: i) ſexp (f (x)) dx > exp ( Sf (x) dx ); 1 ii) ſexp (f (x)) dx < exp ( Sf (x) dx Explain your answer. b) when do we have equality in a)? Explain your answer.
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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(just b)
![Let f be an integrable function on [0, 1] .
a) Which of the following inequalities is true:
1
i) ſexp (f (x)) dx > exp ( Sf (x) dx ) ;
ii) ſexp (f (x)) dx < exp
'f (x) dx
Explain your answer.
b) when do we have equality in a)? Explain your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd02ff7d5-f08d-4df5-9df9-a58ad10b1343%2Fe63a32d2-bdd3-46fc-a5c7-2e6cd6dd71ad%2Fx8mio38_processed.png&w=3840&q=75)
Transcribed Image Text:Let f be an integrable function on [0, 1] .
a) Which of the following inequalities is true:
1
i) ſexp (f (x)) dx > exp ( Sf (x) dx ) ;
ii) ſexp (f (x)) dx < exp
'f (x) dx
Explain your answer.
b) when do we have equality in a)? Explain your answer.
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