June 25th, 2017, 03:37 PM  #1 
Newbie Joined: Jun 2017 From: Tennessee Posts: 1 Thanks: 0  Circumference of an Ellipse
Approximate, within an error of 0.001 units, the circumference of the ellipse given by the equation (x/3)^2+(y/2)^2=1 
June 25th, 2017, 04:19 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,663 Thanks: 1328 
$x = 3\cos{t}$ $y = 2\sin{t}$ $\displaystyle C = 4\int_0^{\pi/2} \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt} \right)^2} \, dt$ $\displaystyle C = 4 \int_0^{\pi/2} \sqrt{9\sin^2{t}+4\cos^2{t}} \, dt \approx 15.865$ 
July 1st, 2017, 11:07 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,829 Thanks: 753 
The reason the problem asks you to "Approximate, within an error of 0.001 units" is that we cannot do this integral "analytically". It is one of a class of integrals called "elliptic integrals". I remember, many, many years ago seeing. in a University library, an entire shelf of, I think, 20 large volumes giving numerical values of the elliptic integrals. You will need to complete this problem using some numerical integration method.

July 1st, 2017, 11:17 AM  #4  
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  Quote:
 
July 1st, 2017, 05:45 PM  #5 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,829 Thanks: 753  

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