# Integral of a function and its inverse - Real analysis

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#1
The following questing concerns a strictly increasing function f on [0,a] st f(0)=0

I think I've done the first part, the second I could do with some help please. I'm pretty sure there's a typo in the hint (first inequality on the final line).Thanks
0
6 years ago
#2
Yea, pretty sure it's a typo as well. If it isn't the typo then the last inequality should be I believe.
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6 years ago
#3
(Original post by alexmufc1995)
The following questing concerns a strictly increasing function f on [0,a] st f(0)=0

I think I've done the first part, the second I could do with some help please. I'm pretty sure there's a typo in the hint (first inequality on the final line).Thanks
I guess they're inviting you to consider the integrals if I've read the inequalities properly.
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#4
(Original post by atsruser)
I guess they're inviting you to consider the integrals if I've read the inequalities properly.
I agree, but I still can't work out how to use the hint to get the required inequality
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6 years ago
#5
(Original post by alexmufc1995)
I agree, but I still can't work out how to use the hint to get the required inequality
Doesn't it follow trivially from part (a) + the inequality that they suggest?
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#6
(Original post by atsruser)
Doesn't it follow trivially from part (a) + the inequality that they suggest?
But I need to show the inequality they suggest? That's really what I don't understand how to do.

That is, I know how to complete the question once I've established the hint inequality holds.
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6 years ago
#7
(Original post by alexmufc1995)
But I need to show the inequality they suggest? That's really what I don't understand how to do.

That is, I know how to complete the question once I've established the hint inequality holds.
It's a bit late for this kind of stuff, but I think:

1. Show that
2.

or something along those lines.
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