May 18th, 2014, 03:42 PM  #1 
Member Joined: Apr 2014 From: australia Posts: 68 Thanks: 32  double integral problem
Hi, Trying to solve the attached double integral, not sure if I have done it correctly, can someone check? (see attachment). thanks 
May 18th, 2014, 07:06 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra 
I get almost the same result, you've just made an error in the last step. $$r^2 + 1 \ne 0 \; \text{where $r = 0$}$$ 
May 18th, 2014, 08:13 PM  #3 
Member Joined: Apr 2014 From: australia Posts: 68 Thanks: 32 
thanks for checking, could please show me your working at the point where i have made a mistake. thanks for your time. 
May 18th, 2014, 08:25 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra 
I worked the integral slightly differently, but your error isn't in the integral. You have $$I = \left. \frac{\pi}{4}\left[ \left(r^2 + 1\right) \ln{\left( r^2 + 1 \right)}  \left( r^2 + 1 \right) \right] \right_0^3$$ Which I agree with. But the next line (the last one is wrong). I'm reasonably sure that you evaluated the expression at $r = 3$ correctly, but I think you got 0 at $r = 0$, which is not correct. 
May 18th, 2014, 08:35 PM  #5 
Member Joined: Apr 2014 From: australia Posts: 68 Thanks: 32 
yes you're right, thanks for your help. I get 11.02 now.
Last edited by harley05; May 18th, 2014 at 08:39 PM. 
May 18th, 2014, 08:51 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,502 Thanks: 2511 Math Focus: Mainly analysis and algebra 
Me too.


Tags 
double, double integral, integral, problem 
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