You are not logged in.
#1 2009-09-15 07:58:19
- bobbym
- Administrator
Offline
Integral and inequality
Hi;
Evaluate this integral:
Prove the inequality:
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#2 2009-09-15 08:12:44
- mathsyperson
- Moderator
Offline
Re: Integral and inequality
Are we allowed to express the LHS of the inequality as a Taylor series? If so, the problem becomes trivial.
Why did the vector cross the road?
It wanted to be normal.
#3 2009-09-15 08:28:28
- bobbym
- Administrator
Offline
Re: Integral and inequality
Hi mathsyperson;
Thats how I would do it. But in this Putnam problem book he doesn't use that method. Why, I can't say.
Last edited by bobbym (2009-09-15 09:42:02)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2009-09-15 10:43:51
- JaneFairfax
- Legendary Member
Offline
Re: Integral and inequality
Ever seen this theorem?
Let be convex and differentiable. Then
So you just put and .
(What I’m saying is that no point on a convex and differentiable curve lies below the corresponding point on a straight line that is tangent to any part of the curve.)
PS: I just looked up Wikipedia. This theorem is stated there without proof.
Last edited by JaneFairfax (2009-09-15 10:56:36)
#5 2009-09-15 11:07:40
- JaneFairfax
- Legendary Member
Offline
Re: Integral and inequality
mathsyperson wrote:
Are we allowed to express the LHS of the inequality as a Taylor series? If so, the problem becomes trivial.
bobbym wrote:
Thats how I would do it.
The inequality holds for
as well, in which case the method will not be trivial for .And note that there is an apostrophe in That’s.
#6 2009-09-15 14:21:12
- bobbym
- Administrator
Offline
Re: Integral and inequality
Hello Jane;
Jane wrote:
The inequality holds for
as well, in which case the method will not be trivial for .
But the problem states x > 0 and mathsy is right using the expansion of e^x makes it trivial.
Jane wrote:
And note that there is an apostrophe in That’s.
That is true Jane, poor typing and high speeds, a lethal combination. Thanks for the correction.
Jane wrote:
Ever seen this theorem?
Yes Jane, I have heard of that theorem but I forgot it.
Last edited by bobbym (2009-09-15 16:23:55)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#7 2009-09-16 05:36:20
- bobbym
- Administrator
Offline
Re: Integral and inequality
Hi;
The inequality was the easy one. Now how about the integral it is even easier. If you start substituting you will go mad.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#8 2009-09-25 22:11:45
- bobbym
- Administrator
Offline
Re: Integral and inequality
Hi;
Another integral this one is also easy:
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#9 2009-09-25 23:06:15
#10 2009-09-26 09:13:48
- bobbym
- Administrator
Offline
Re: Integral and inequality
Hi Jane;
Last edited by bobbym (2009-09-26 09:14:14)
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#11 2010-09-29 05:36:42
- 123ronnie321
- Full Member
Offline
Re: Integral and inequality
bobbym wrote:
Hi;
Another integral this one is also easy:
(e^2x)/2 - (e^-2x)/2
#12 2010-09-29 05:41:17
- 123ronnie321
- Full Member
Offline
Re: Integral and inequality
bobbym wrote:
Hi;
Evaluate this integral:
Prove the inequality:
1/2[x - log(sinx + cosx)]
#13 2010-09-29 06:24:31
- bobbym
- Administrator
Offline
Re: Integral and inequality
Hi 123ronnie321;
Yes that is almost correct!
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#14 2011-03-30 22:05:19
- gAr
- Star Member
Offline
Re: Integral and inequality
Hi bobbym,
Evaluate this integral:
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#15 2011-03-30 22:49:54
- bobbym
- Administrator
Offline
Re: Integral and inequality
Hi gAr;
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#16 2011-03-30 23:07:52
- gAr
- Star Member
Offline
Re: Integral and inequality
Thank you!
"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
#17 2011-03-30 23:13:01
- bobbym
- Administrator
Offline
Re: Integral and inequality
HI gAr;
You are welcome.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.