Quiz: calculating a definite integral
01-03-2014, 11:42 AM
Post: #34
 Bunuel66 On Vacation Posts: 29 Joined: Jan 2014
RE: Quiz: calculating a definite integral
(01-03-2014 07:03 AM)Thomas Klemm Wrote:
(01-03-2014 06:08 AM)walter b Wrote:  there can be only one correct.
Use integration by parts to get: $$\int_{0}^{1}x^n\log(x)^p dx=-\frac{p}{n+1}\int_{0}^{1}x^n\log(x)^{p-1}dx$$
Iterate starting with $$p=n$$ until you end up with: $$\int_{0}^{1}x^n dx=\frac{1}{n+1}$$.
You can figure out by yourself which is correct.

Sorry, I made a mistake while copying from my paper: too late in the night and with a headhache ;-)The right expression is with n+1, it is now corrected.
That said 0⁰ is not a problem, it is quite easy to show that it is 1.

From a strict mathematical standpoint, I'm a bit puzzled as the Taylor expansion used seems a bit unjustified:
-the expansion of e^u(x) is not a sum of power of u(x) but a sum of successive derivatives of e^u(x) which doesn't seems to be the same.
-the first derivative of the function is not defined at 0, then the expansion can't converge, one could have used and expansion around 1 to go that way.

I do agree that the sum gives the right result but I don't grasp a rigorous proof.

If somebody has some light....

Regards
 « Next Oldest | Next Newest »

 Messages In This Thread Quiz: calculating a definite integral - Thomas Klemm - 12-30-2013, 09:37 PM RE: Quiz: calculating a defined integral - John Smitherman - 12-30-2013, 10:46 PM RE: Quiz: calculating a defined integral - W_Max - 12-30-2013, 11:44 PM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 06:37 AM RE: Quiz: calculating a defined integral - Namir - 12-31-2013, 04:24 AM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 04:56 AM RE: Quiz: calculating a defined integral - walter b - 12-31-2013, 08:54 AM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 09:14 AM RE: Quiz: calculating a defined integral - walter b - 12-31-2013, 10:12 AM RE: Quiz: calculating a defined integral - Paul Dale - 12-31-2013, 07:13 AM RE: Quiz: calculating a defined integral - peacecalc - 12-31-2013, 10:24 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-01-2014, 10:31 PM RE: Quiz: calculating a definite integral - walter b - 01-02-2014, 08:11 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014, 06:09 PM RE: Quiz: calculating a definite integral - Gerson W. Barbosa - 01-02-2014, 11:34 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014, 01:14 PM RE: Quiz: calculating a definite integral - Gerson W. Barbosa - 01-03-2014, 01:49 AM RE: Quiz: calculating a defined integral - peacecalc - 12-31-2013, 10:57 AM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 01:14 PM RE: Quiz: calculating a definite integral - Gerson W. Barbosa - 01-16-2014, 08:21 PM RE: Quiz: calculating a defined integral - Paul Dale - 12-31-2013, 01:29 PM RE: Quiz: calculating a defined integral - walter b - 12-31-2013, 02:16 PM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 06:01 PM RE: Quiz: calculating a definite integral - Ángel Martin - 01-03-2014, 07:20 AM RE: Quiz: calculating a defined integral - peacecalc - 12-31-2013, 02:20 PM RE: Quiz: calculating a defined integral - Thomas Klemm - 12-31-2013, 05:55 PM RE: Quiz: calculating a definite integral - peacecalc - 01-02-2014, 08:36 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014, 09:42 AM RE: Quiz: calculating a definite integral - peacecalc - 01-02-2014, 10:12 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-02-2014, 11:55 AM RE: Quiz: calculating a definite integral - Bunuel66 - 01-02-2014, 11:39 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 05:18 AM RE: Quiz: calculating a definite integral - walter b - 01-03-2014, 06:08 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 07:03 AM RE: Quiz: calculating a definite integral - Bunuel66 - 01-03-2014 11:42 AM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 12:47 PM RE: Quiz: calculating a definite integral - Bunuel66 - 01-03-2014, 01:29 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 02:50 PM RE: Quiz: calculating a definite integral - Bunuel66 - 01-03-2014, 05:38 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 08:39 PM RE: Quiz: calculating a definite integral - Bunuel66 - 01-03-2014, 09:04 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-06-2014, 10:28 AM RE: Quiz: calculating a definite integral - Bunuel66 - 01-07-2014, 06:12 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-09-2014, 07:45 AM RE: Quiz: calculating a definite integral - W_Max - 01-03-2014, 08:03 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-03-2014, 09:32 PM RE: Quiz: calculating a definite integral - W_Max - 01-03-2014, 11:08 PM RE: Quiz: calculating a definite integral - Thomas Klemm - 01-14-2014, 02:31 PM RE: Quiz: calculating a definite integral - walter b - 01-14-2014, 02:53 PM

User(s) browsing this thread: 1 Guest(s)