September 13th, 2018, 11:04 AM  #11 
Senior Member Joined: Sep 2015 From: USA Posts: 2,404 Thanks: 1306 
I think $2a \to a$ mistakenly somewhere along the way as well.

September 13th, 2018, 01:04 PM  #12  
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  Quote:
Look at the beginning. With new axes at the center of the circle: x'=x+a $\displaystyle \sqrt{2a+x} = \sqrt{2a+(x'a))}= \sqrt{a+x'}$ Then I did calculation in the new coordinate system without primes because it would have been a pain to carry them through. In above quote I corrected the minus sign at the end.  
September 13th, 2018, 01:48 PM  #13 
Senior Member Joined: Sep 2015 From: USA Posts: 2,404 Thanks: 1306 
afk in a pool of blood... don't call 911.... just let me rot here

September 13th, 2018, 04:12 PM  #14 
Global Moderator Joined: Dec 2006 Posts: 20,464 Thanks: 2038 
Although romsek's method may seem to work with the aid of Mathematica, doing the integral in polar coordinates by hand is cumbersome and tricky. Special functions aren't needed. It's better to stick with Cartesian coordinates. Eventually, zylo got quite close to a correct answer, but is still not quite there. 
September 14th, 2018, 10:48 AM  #15  
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  Quote:
$\displaystyle I=2\int_{a}^{a}\sqrt{ax}dx= \frac{4}{3}\sqrt{(ax)^{3}}\biggr\rvert_{a}^{a} = \frac{8\sqrt{2}}{3}a^{\frac{3}{2}}$  

Tags 
double, integral, solve 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Solve double integral by converting to polar coordinates  DakshD  Calculus  1  November 8th, 2016 11:38 AM 
Double integral, repeated integral and the FTC  Jhenrique  Calculus  5  June 30th, 2015 03:45 PM 
Double Integral, for whoever wants to solve it!  mathbalarka  Calculus  9  May 28th, 2012 05:32 AM 
integral of double integral in a region E  maximus101  Calculus  0  March 4th, 2011 01:31 AM 
integral of double integral in a region E  maximus101  Algebra  0  December 31st, 1969 04:00 PM 