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#1 2014-12-05 21:12:43
- clover
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- Registered: 2014-12-05
- Posts: 3
integration problems urgent!
thx a lot~
Last edited by clover (2014-12-05 21:17:05)
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#2 2014-12-05 21:17:09
- Bob
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- Registered: 2010-06-20
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Re: integration problems urgent!
hi clover,
I cannot access that link. Browser still trying to download.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2014-12-05 21:17:52
- clover
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- Registered: 2014-12-05
- Posts: 3
Re: integration problems urgent!
hi bob,
i have edited the post, c if u can c it now
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#4 2014-12-05 21:18:37
- Bob
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Re: integration problems urgent!
Yes, that's better. Just need a moment to read it.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#5 2014-12-05 21:30:02
- Bob
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- Registered: 2010-06-20
- Posts: 10,140
Re: integration problems urgent!
Thoughts on Q1.
If f(t) = e^t then g(x) = e^x - 1
Then g(x^2) has the property.
Not sure if I can do the others. Thinking............
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#6 2014-12-05 21:31:19
- Bob
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- Registered: 2010-06-20
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Re: integration problems urgent!
Whoops only ok for x>0. Back to the drawing board.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#8 2014-12-06 01:25:01
- Bob
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- Registered: 2010-06-20
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Re: integration problems urgent!
hi zetafunc,
I'm so pleased you're having a go at this. I'm really stuck.
If f(t) = k then g(x) = kx => g(x^2) = kx^2, which isn't 'upward' for x<0
As e^x has the property I'm trying to make a piecewise function ie. in two parts for negative and positive x. wait a mo. Can I adapt yours ?
Say, f(t) = k for t > 0 and -k for t < 0
t > 0 as before.
t < 0 => g(x) = -kx => g(x^2) = -kx^2. Drat! It's not concave for all x.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#9 2014-12-06 05:29:11
- Bob
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- Registered: 2010-06-20
- Posts: 10,140
Re: integration problems urgent!
I cannot believe how stupid I have been all day. The answer has been staring me in the face! 
I had assumed that 'concave upward function' meant the function was to be 'increasing'. It has just dawned on me that this interpretation would make the question impossible for:
so g(x^2) is an even function => the y axis is a line of symmetry => it cannot be increasing.
So I now look for an alternative meaning to 'concave upward'. If it just means U-shaped then my answer in post 5 is good and so is zetafunc's in post 7. Sorry. 
So I'll take Q1 as done, and think about Q2.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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