Subject: wrong integration - depending on approach
From: Joerg Rauh
Date: Sat, 31 Dec 2011 06:06:55 -0800 (PST)
Using the indefinite integral,after simplifying, I get :
(log((sqrt(x+1)+sqrt(x))^3/(sqrt(x+1)-sqrt(x))^3)+sqrt(x+1)*(4*x^(3/2)-6*sqrt(x)))/8
Definig a function f(x) with this expression and doing
f(1)-f(0)=(log((sqrt(2)+1)^3/(sqrt(2)-1)^3)-2^(3/2))/8
turns into numeric 0.307476799671383 as expected.
For comparison: romberg(x^1.5/(x+1)^0.5,0,1)=0.30747833750506?
Regards
Joerg
________________________________
From: t t <lan1967 at mail.ru>
To: maxima <maxima at math.utexas.edu>
Sent: Saturday, December 31, 2011 9:32 AM
Subject: wrong integration
Hello, dear users!
I tried to integrate the following integral and got the negative answer. Surely the answer is wrong.
Here:
integrate(x*x^0.5/(1+x)^0.5,x,0,1)
-2^(3/2)
Thank you for your attention
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